Aflagpole that was originally 24 feet tall has cracked 9 feet from the ground and has fallen as if hinged. find out how far from the base of the flagpole the top of the flagpole touched after it had fallen.

The top of the flag pole touched the ground 12 feet from the base.

Since it cracked 9 feet from the base, 9 is the vertical leg of the right triangle formed.  The rest of the flagpole, 24-9=15, is the hypotenuse, as it is slanted down to the ground.  The missing side is the horizontal leg, which we will call b:

9²+b²=15²
81+b²=225

Subtract 81 from both sides:
81+b²-81=225-81
b²=144

Take the square root of both sides:
√b²=√144
b=12

Does the problem say y=x+4?