Let $|a|=4$ and $|b|=2$ be in group $G$ with $a^3b=ba$. Find $|ab|$. Let $|a|=4$ and $|b|=2$ be in group $G$ with $a^3b=ba$. Find $|ab|$.
Are those absolute values? Or something else?

As a hint, start taking powers of $ab$. First note that if
$$ab = e \implies a = b^{-1} \implies a^2 = 2$$
contradicting that $|a| = 2$. Next we have
$$(ab)^2 = abab = a(a^3b)b = a^4 b^2 = ...?$$
