Can we compose two simple functions?

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Let \[f(x)=x+1\qquad\text{and}\qquad g(x)=2x.\]

4. Let \(m\geq0\) be an integer. How many different ways of combining the functions \(f\) and \(g\) are there that result in the function \(4x+4m\)?

Can we use part (iii) of this question here? How many times do we need to do \(g\)? And \(f\)?