No, you probably can't. To make biogas on any reasonable scale is at least a village-scale thing; a single family/household cannot easily produce sufficient raw-material to manufacture useful amounts of methane unless you commit to growing biomass just for conversion. (See also another comment below where livestock are involved, so another path to a sufficiency of raw material.)
I was very keen on the idea of making my own biogas (for cooking) when starting out in my self-sufficiency efforts some >25y ago, and the entire sewage system is designed to make conversion to biogas production easy, but the reality is it's just not ever going to produce any significant quantity of methane without some serious supplementation. Add to that, biogas digesters slow down significantly in Winter, even here where we never get freezing temps. In places that experience serious Winters you need to figure out ways to heat(!) the digester to keep it working lest the raw material inputs back up and cause... a mess that will thaw in Springtime with (cough) challenging results.
Growing up, my grandparents' house had a biogas plant, powered by cowdung (they had anywhere between 6 and 8 cows and bulls at the time). Looked something like this: https://www.peda.gov.in/nnbomp
Most of the cooking and some of the lighting for the house was done using this thing. Most of the bigger houses in the village had one.
You can probably do that, but don't delude yourself that you're doing anything for the environment.
Methane itself is a very potent greenhouse gas. Everything you do with methane is only environmentally friendly if you have a very low leakage rate. Whatever homegrown DIY biogas facility you're creating very likely does not do that.
Ideally your kitchen waste would go into a facility that properly handles it and will use it for energy production, but in a properly controlled environment (and if that energy production is biogas by avoiding methane leakage as good as possible).
Of course whether that happens depends a lot on where you're living.
Although our municipal green waste gets converted to compost, I recently found out that there is a food waste to energy plant in my city [1]. Going by their numbers, a home can be powered for a year with 25 tonnes of food waste, or 70 kg a day.
The two largest sewerage treatment plants also capture and generate electricity from biogas [2].
I think in Germany this is pretty standard (both turning organic waste into biogas and collecting biogas at sewage treatment facilities).
And tbh not treating organic waste as some form of resource should be considered a scandal these days, and the only valid discussion to be had should be how to use it (my bet would be that in the long term that will be chemicals and not energy). There is legitimately a lot of talk about the landuse issues of bioenergy, but using organic waste doesn't have any of those problems. It should be an absolute nobrainer.
Household waste either goes to commercial composting plants (where the methane produced most likely escapes) or to sanitary landfills, where the reduced biological activity means that the scraps degrade at a much slower rate, but do eventually reduce to methane and other lipids, though possibly at the scale of millennia or longer.
Biogas is by definition a product of excess biomass production. The net potential can be estimate by the net agricultural (and perhaps forestry) primary production within a country.
To a rough first approximation based on food intake, biomass is the residual of undigested food caloric energy in the waste stream, which I believe runs at about 25% of the input calories.
You can estimate this for a population by taking roughly 2,000 kilocalories/day * population * 0.25. Ignoring any collection or processing losses, for the US this translates to about 700,000 GJ, 110,000 barreloil, or 200 GWh electricity (assuming no generation or transmission losses, in actuality about 1/3 this amount).
Actual US energy consumption is closer to 45 million barreloil day (equivalent, only 18.3 million barrels of actual oil), or roughly 400 times the maximum amount of energy available in food waste.
There may be other biomass wastestreams available (say: the input feedstock for livestock, pork, dairy, and poultry), though this won't add up to the 400-fold increase necessary as typically the trophic loss is about 10x in a given foodchain level. Even were all US food consumption in the form of animal products, the wastestream would be 40x short of present energy consumption levels.
It's not clear if the artist here is aware of what they're demonstrating, but the process of methane harvesting employed is not dissimilar to how fossil fuels formed in the first place, with biomass settling to the bottoms of shallow seas and, over the course of hundreds of millions of years, being transformed to petroleum and natural gas.
We're presently consuming that bounty at roughly 5 million times its rate of formation. The fact that it takes 8 hours to produce fuel sufficient for 20km of travel is actually millions of times more efficient than the net energy cost of fossil fuels.
Jeffrey S. Dukes, "Burning Buried Sunshine" (2003) details this with exquisite clarity.
Anaerobic digestion of food and green waste yields ~0.22 toe/tonne of biogas, and manure yields up to 0.04 toe/tonne [1]. (toe = tonnes of oil equivalent)
Australia wastes 300 kg/year/capita of food [2] (across the entire supply chain, from farm through fork)
Americans generate 90 kg/year/capita of yard waste [3]
That's 1.07 kg/day, for 0.24 kg of oil equiv.
The average adult produces ~0.4 kg/day of manure [4], for 0.02 kg of oil equiv.
All up that's 0.26 kgoe/day, or 0.3 L [5] of petrol.
The most efficient scooter I could find (Honda Activa-i) does around 70 km/L (165 mpg)
So optimistically, you could generate 21 moped kilometers per day of biogas. In more normal units, that 3 kW/h or 11 MJ.
I was very keen on the idea of making my own biogas (for cooking) when starting out in my self-sufficiency efforts some >25y ago, and the entire sewage system is designed to make conversion to biogas production easy, but the reality is it's just not ever going to produce any significant quantity of methane without some serious supplementation. Add to that, biogas digesters slow down significantly in Winter, even here where we never get freezing temps. In places that experience serious Winters you need to figure out ways to heat(!) the digester to keep it working lest the raw material inputs back up and cause... a mess that will thaw in Springtime with (cough) challenging results.