Consider $-6a^{4}b^{4}+2a^{3}b^{4}+3a^{2}b^{3}-ab^{3}$. Factor out $ab^{3}$.
$$ab^{3}\left(-6a^{3}b+2a^{2}b+3a-1\right)$$
Consider $-6a^{3}b+2a^{2}b+3a-1$. Do the grouping $-6a^{3}b+2a^{2}b+3a-1=\left(-6a^{3}b+2a^{2}b\right)+\left(3a-1\right)$, and factor out $2ba^{2}$ in the first and $-1$ in the second group.
$$2ba^{2}\left(-3a+1\right)-\left(-3a+1\right)$$
Factor out common term $-3a+1$ by using distributive property.
