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?

Those are orders of elements.
The order of an element $g\in G$, denoted $|g|$, is defined as the smallest positive integer $n$ such that $g^n = e$, the identity element of the group.
So, in your question, we know that $a^4 = e$ (and no smaller power will do), and that $b^2 = e$ (and no smaller power will do).
This is enough to conclude that $|ab| = 2$, because $(ab)^2 = abab = a(ba)b = a(a^3b)b = a^4b^2 = e\cdot e = e$, and $ab$ cannot be the identity, because otherwise a would be the inverse of b, and so have the same order.
