Find all congruences classes x modulo 14 that satisfy the equation 4x 10 (mod 14) Because d =gcd(4, 14) = 2 and 2 | 12, we expect there to be d = 2...

Find all congruences classes x modulo 14 that satisfy the equation 4x ≡ 10 (mod 14) Because d =gcd(4, 14) = 2 and 2 | 12, we expect there to be d = 2 solutions. To find these we divide through by d = 2: 2x ≡ 5 (mod 7) 2x ≡ 12 (mod 7) Since gcd(7, 2) = 1, we can divide by 2. x ≡ 6 (mod 7) Thus the two solutions modulo 14 are the classes [6] and [6 + 7] = [13]

This is a completed example, I just would like an explanation. I get lost at 2|12. Where did 12 come from?