The problem is that you have't specifically set up a "coordinate system". That is, you have not stated exactly where x= 0, y= 0 will be and which directions are positive.

"'A girl throws a ball form point A at the top of a cliff. The point A is 8 m above a horizontal beach. The ball is projected with a speed of at an angle of elevation of 45 degrees. By modelling the ball as a particle moving freely under gravity, find the horizontal distance of the ball from A when the ball is 1 m above the beach.

I can solve this by substituting into the equation given in the first part if take the displacement y to be -7 m"

Do you mean -8 m? There is no "7" distance mentioned here. If so then you are taking y= 0 to be at the "horizontal beach" and, though it strikes me as strange, y increasingdownward. In this case "1 m above the beach" would be y= -1.

What the signs are is pretty muchyourchoice. It depends upon your choice of a coordinate system.