$f(n)=4^n*n$ $g(n)=6^n$, prove or disprove $f \in o(g)$

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$f(n):=4^{n}*n$ and $g(n):=6^n$

so we need to show that $f(n) \leq c g(n)$

I tried to find upper and lower bounds:

$\frac{4^{n}*n}{6^n} = \frac{4^{n}*n}{(3/2)^n4^n} = \frac{n}{(3/2)^n} $

$\frac{n}{(2)^n}=\frac{n}{(4/2)^n} \leq \frac{n}{(3/2)^n} \leq \frac{n}{(2/2)^n} = n$

However do not think that my approach is useful so any hint would be helpful.