If A(7;-2) and B(-3;6) find the value of y if T(-3;y) and AT=AB

I just don't know what they want

Draw a graph, I think that will help. They want you to find a point T such that the distance from A-T equals the distance from A-B. Both points B & T will lay on the same vertical line x = -3, so this makes it easier.

Look at your graph. Starting at A, go left (along the line y = -2) to the line x = -3, then go up to B. Count the movement up, from -2 to 6, you moved up 8.

Now repeat this process, but when you get to the line x = -3, move DOWN 8. From -2 down 8 gets us to the point -10.

So your final point is (-3, -10), y = -10.

AT^2 = {7-(-3)}^2 + {-2-y}^2 and
AB^2 = {7-(-3)}^2 + {-2-6}^2; As AT = AB or AT^2 = AB^2, So y = 6