Which point is on the line that passes through point h and is perpendicular to line fg? (-6,10) (-2,-12) (0,-2) (4,2)

Perpendicular lines have slopes that are negative reciprocals. 
Since the slope of line FG is 3/4, you are looking for a slope that is -4/3.

the slope formula is m= (y₂-y₁)/(x₂-x₁)

you are given one point of the formula (6, -6) so you just need to plug in the options until you get an answer of -4/3

A) (-6 , 10)
    m= (10-(-6)/(-6-6)
   m = 16/-12
   m=  -4/3

after getting a slope of -4/3 you can conclude that the answer is 
A) (-6, 10)

hope this helped!

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