How many solutions does $4x \equiv 8 \pmod{12}$ have among $x = 0, 1, \dots, 11$?

Explanation

1. 01

   $\gcd(4, 12) = 4$, and 4 divides 8, so there are exactly 4 solutions modulo 12.

2. 02

   They are $x = 2, 5, 8, 11$: each gives $4x$ = 8, 20, 32 or 44, all $\equiv 8$.