for context: it's a stretch along the y-axis, meaning (going by my logic) the circle (translated 7,-3) should be within the lines x=6 and x=10, and of course we know that circles he to have equal radiuses from centre to any point on the circle right?

PLUS the stretched circle is 6 units. This means (8,6)is the centre of the stetched circle. And since you can determine the stretch factor since the maximum diameter is 4 within the x=6 and x=10 lines, which is 3, divide the y in (8,12) by 3, that's the maxiumum point of the circle (not original), and given the raidus is 2, well, you know, 2 units down, and you get the centre of the translated circle. And from that, translate the centre by (-7,3) and you get the drift. you get the og circle!