How many solutions does $6x \equiv 12 \pmod{18}$ have among $x = 0, 1, \dots, 17$?

Explanation

1. 01

   $\gcd(6, 18) = 6$ divides 12, so there are exactly 6 solutions modulo 18.

2. 02

   Dividing through by 6: $x \equiv 2 \pmod{3}$, so $x = 2, 5, 8, 11, 14, 17$.