F(x)=-4x^2+7x+6 how do you work this

There actually isn't anything to 'work'.  There's no question there.

The function simply describes the relationship between two numbers.

It says that whatever you pick for the first number, the second number is

    (-4 times the square of the first one) plus (7 times the first one) plus (6) .

Your teacher may have assigned you something to do with the function,
like draw the graph of it, or find its maximum value (2.9375), or find where
it crosses the x-axis (2.381 and -0.63) or the y-axis (6).

But we can't tell what you've been assigned to do with it.  The function alone,
just as you've posted it, isn't asking a question, and doesn't call for any work.

What does h hours mean

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.