Ummm... why don't you just run two extension cords. One from one circuit and one from another circuit?
Am I missing something?
Why are you attempting to mix the two circuits?

Oh ... and I guess to answer your question ... there is no legal/safe/possible way to do what you'd like to do. Somehow mingling two 20A circuits will never get you a 40A circuit.

No need to be snarky. I said I'm not familiar with AC systems. In a DC circuit you can wire two power sources in parallel to get double amperage from the same voltage. If you're going to tell me that AC doesn't work that way then I'll find another solution.

I didn't mean to be snarky. I genuinely don't understand why 2 circuits won't satisfy your needs. Why does it have to be one?

It won't even necessarily work with DC. In fact, the reason it won't work is pretty much the same as with DC. First, note that half the 120V circuits in your house are 120V on one side of ground and the other are 120V on the other side of ground. Obviously the only two ways of combining this would be either a disaster (like shorting two batteries together) or it would yield a single, same amperage, 240V circuit.

The other reason is that these aren't two fixed voltage, 20A sources. They're a much larger source that has a over current device that will shut them down at 20A. Now given the fact your house wiring past the breaker and your extension cords are unlikely to have exactly the same resistance means, that you'll likely flow 20A on one side tripping the breaker before you get 20A on the other side. Of course, once one breaker trips, the other will in short order as the whole load switches to that side.

As pointed out the only sane solution is divide your loads. Note however what is going to hurt you running a wood shop in the garage on extension cords (been there, done that), is not so much the lack of current capacity on the individual branch circuits (within reason), but the fact your extension cord is most likely rather small and hence (you'll understand this from DC) higher in resistance which means that your delivered voltage will be significantly less than 120V. However, you can buy 12G extension cords (oddly they call these 30A cords) or make your own by buying some suitably large cordage and adding your own connectors.

Of course, the only real long term happiness is to install a larger feeder and put a small sub panel in the garage to feed the various equipment. Some day you'll get a 3HP something or other and need either 30A 120 or 20A 240.

Paralleling two 20A circuits will get you a more-than-20A circuit (albeit not legally or 100% safely). It won't equal out to 30A, since, as another poster noted, the impedances won't match and one circuit will be providing more of the current than the other... but the other will still be providing SOME current, meaning that the new trip-point will be higher than a single 20A breaker.

That said, I do agree with the others that two seperate extension cords will be best.

If you've got a four-wire socket for your electric stove or dryer, you could purchase appropriate-rated cable and a breaker box and essentially construct a temporary portable subpanel to plug into that... legal? debatable, enforceable? no. safe? that's in the eye of the beholder. I've been running live sound for local bands some ten years now, this is roughly equivalent to what we do when we wind up in a residential setting, and I haven't set anybody on fire yet. Keep your grounds and neutrals seperate the whole way through and wire it up like you would any other subpanel.