f(x)=2.5, g(x)=2x+1 and h(x)=x

and the difference between 2 times the outputs of f and 3 times those of g is 8 less than 4 times the outputs of h

how do i solve for x?

Either

3g(x) - 2f(x) = 4h(x) -8
or
2f(x) - 3g(x) = 4h(x) -8

You don't say which sign to use for the "difference" on the left.

Substitute the appropriate functions and solve whichever is the correct equation to get x.