We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$ $g(x),$ and $h(x)$ are all polynomials in $x.$ If the degree of $f(x)$ is $8$ and the degree of $h(x)$ is $9$, then what is the minimum possible degree of $g(x)$?

Multiplying a polynomial by a (non-zero) constant does not change its degree

So

degree 8 + degree 9 = degree 9

g(x) = degree 9