Each equation equal y, right? So you can substitute 1/2x+6 for y in y=4x-1 (or 4x-1 in y=1/2x+6). Either way, you'll end up with 4x-1=1/2x+6. Then, you just solve for x.
4x-1=1/2x+6
3.5x=5
x=5/3.5
I would suggest leaving it in fraction form considering if you translate it to decimal form it will be a less precise answer.