Mark leaned a 12 foot ladder against the side of his house. the bottom of the ladder was 4 feet from the house. how far up the house was the top of the ladder?

If you stand over there at the end of the house and look back here
at the ladder, you'll see that what Mark has is a right triangle. 

There's a right angle where the side of the house meets the ground,
the base of the triangle is the 4 feet, and the ladder is the hypotenuse.
So we know that

 (length of the ladder)² = (4-ft)² + (height of the top of the ladder)²

         (12-ft)²              = (4-ft)² + (height of the top of the ladder)²

         (144 ft²)  =  (16 ft²) + (height of the top of the ladder)²

Subtract  16ft²  from each side, and you have:

           128 ft² = (height of the ladder)²

Take the square root of each side:

           Height of the ladder = √(128 ft²)  =  11.31 ft.  (rounded)

The correct answer is d. (0,5)