[Math] Find order of element in a quotient group

Question

I'm having trouble figuring out

Find the order of the element $\overline{8} + \langle\overline{6} \rangle$ in the quotient group $\mathbb{Z}_{60} / \langle \overline{6} \rangle$

Answer 1

The elements of $\mathbb{Z}_{60}/\langle \overline{6}\rangle$ are $\langle \overline{6}\rangle$, $\overline{1}+\langle \overline{6}\rangle$, $\overline{2}+\langle \overline{6}\rangle$, $\overline{3}+\langle \overline{6}\rangle$, $\overline{4}+\langle \overline{6}\rangle$, and $\overline{5}+\langle \overline{6}\rangle$. which if these is equal to $\overline{8}+\langle \overline{6}\rangle$? How many times do you have to add that one to itself to get $\langle \overline{6}\rangle$?

There’s no law against doing some actual computations to see what’s going on!