Step 1 :The functions $f$ and $g$ are defined as follows: $f(x)=5x+4$ and $g(x)=2x^{2}-3x$.
Step 2 :We are asked to find the values of $f(-4)$ and $g(-6)$.
Step 3 :To find these values, we substitute $-4$ and $-6$ into the functions $f(x)$ and $g(x)$ respectively.
Step 4 :Substituting $-4$ into $f(x)$, we get $f(-4)=5(-4)+4=-16$.
Step 5 :Substituting $-6$ into $g(x)$, we get $g(-6)=2(-6)^{2}-3(-6)=90$.
Step 6 :So, the final answers are $f(-4)=\boxed{-16}$ and $g(-6)=\boxed{90}$.