How can I find the short circuit current across a and b?
First of all, I strongly recommend actually assigning names (like \$R_1\ldots R_4\$) to your resistors. It makes talking about schematics much easier.

Anyway, when shorting a-b, your 10 Ω becomes irrelevant.

All the current from the current source goes through that short, so while we have to add that current to the total current through the a-b short in the end, it doesn't interfere with the rest of the calculation. So, you build a "helper" circuit.

Thus, all you have to do is calculate the current through R3 in this circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

The voltage across R2 (or across R3) is your v_x; I'm sure you can solve this :)