how much weight can I lift with 3 2x12x20 feet long beam supported by 6x6 post on each shide this is insde a pole barn
Hmmm...this is difficult. I’ve been staring at this for 20 minutes trying to figure out how to answer this...I’ll try. 

Many factors: 1) Design Use, 2) Duration  of Use, 3) Species, 4) Grade, and 5) Exact span.

1) We design BUILDINGS for “working stress”. That is to say, stresses in wood have a “life expectancy “ and we design with a factor of safety. That is to say, we use the ULTIMATE LOAD and then take a factor of safety, usually by a factor of 2 or at least 1.5. 

2) Duration of Load: The industry has learned (through testing) that wood can withstand up to double the DESIGN LOAD for impact loads. They define impact loads as 1) Less than 24 hours for double the load stress, 2) less than 7 days for an additional third, and less than 14 days for an additional 15%. (We use this a lot for buildings in snow zones.)

3) Species: Some species (like Douglas Fir-Larch) can support about double other species (like Southern pine.)

4) Grade: Likewise as for species.

5) Span: Is it really a 20’ span or 19’ span? Beams are designed based on NET CLEAR distance between supports. 

So, based on all that, I’ll give you a range. 6,000 lbs. for Douglas Fir-Larch with a Select Structural grade and a 7 day duration loading...down to 3,200# for Southern Pine with a grade of #3 and with a 7 day duration loading. 

It’s complicated. There are other factors too, but I hope this gets you started.