I was hoping to calculate the thevenin's resistance. Shouldnt there be a shorted wire or something where we ignore a resistor?
I do not which one though..
You're asking the wrong question. The a and b terminals and arrow in your circuit indicate that the you are looking into the system at terminals a and b such that the 4 ohm resistor is a load. That means you remove the 4 ohm resistor. You REMOVE it, you don't ignore it. Removing means just that. You remove it and terminals and and b become open.
We turn the voltage source off when calculating. We "ignore" it and set it to 0V which is the same as a short. Turning off a current source is setting it to 0A and that would be an open circuit instead.
I get 10 ohm if I do all this.
I would not get too hung up on not needing to redraw the circuit. We are all redrawing it, whether it is in our head or on paper. The method is no different. It just takes some experience to recognize what something is without needing to draw it down.
If two resistors share the same node at each end, they are in parallel and we just successively block resistors together like this until we get something where all the remaining resistors are in a simple series or parallel combination that we can do math on. Just like you do when you re-draw, we just don't write down all the steps because we are familiar enough that we don't need to.
In this case, I stared at it for a bit and went:
0. Set voltage source to 0V or a short and stare at it for a bit searching for any two resistors can be blocked together immediately in parallel or series.
1. I only find one: 60 || 12 so I block them together.
2. Try to block (60||12) with 20 in series or parallel...nope that won't work.
3. Notice that 60||12 and 10 can be immediately blocked together in series so I do that.
4. Now all that is left is 20 in parallel with the block (60||12 + 10)
5. I end up with 20 || [10 + (60 || 12)]
I could have redrawn it or written it down, but I kept track of the single group of resistors on a calculator and kept adding it to things I come across while remembering what I already accounted for in the diagram. So don't worry about needing to redraw it.