H(x) = g(f(x))

Replace the f(x) in g(f(x)) by 4x-5, since we are given that f(x) = 4x-5,

H(x) = g(f(x)) = g(4x-5)

Now we need to find g(4x-5)

To do that, take out the x's in

   g(x) = 2x² - x 

and replace them by empty parentheses (    ):

g(    ) = 2(    )² - (    )

Next fill in the empty parentheses with 4x-5

g(4x-5) = 2(4x-5)² - (4x-5)

So we have

H(x) = g(f(x)) = g(4x-5) = 2(4x-5)² - (4x-5)

Now simplify the right side as 32x² - 84x + 55
 
Answer: H(x) = 32x² - 84x + 55

Edwin