The graph shows that f(x) = 3x is translated horizontally and vertically to create the function g(x) = 3x – h + k. what is the value of h?

The Blue graph is the graph of 

Notice that the blue graph is shifted 2 units up, and 2 units right.

The 2 units shift up is clear. To notice the shift to the right. notice the slight increase of the blue graph at -2, and of the red graph at 0.

shifted 2 units right is  because a shift of 2 units right of any function f(x) is f(x-2).

shifted 2 units up is 

So the function of the red graph is 

h=2, k=2

Absolute value graph shifted point 5 up