Find all six solutions to 12x = 24 mod 30(= is congruence not equality...)

Book says to use this theorem:

Supposed divides a, c, m. Then every solution of

(a/d)x =(c/d) mod (m/d)

corresponds tod distinct solutions (modulo m) of

ax = c mod m:

Not sure how to show this because it seems to me that there would be infinite solutions. How do I do this?