Here is the solution they've given us for (a):

So, how did they get from "196+9x" to "6-x"? I know that 196 mod 10 = 6, but why did they change "9x" to "-x"? What did they do to it?We have to solve:

7 × 2 + 3 × 1 + 9 × 1 + 7 × 8 + 3 × 7 + 9 × 2 + 7 × 9 + 3 × 4 + 9 × x = 0 mod 10

196 + 9x = 0 mod 10

6 − x = 0 mod 10

x = 6

Also this is the given solution to part (b):

228 + 3x = 0 mod 10

8 + 3x = 0 mod 10

3x = -8 = 2 = 12 mod 10

x = 4

I know that 228 mod 10=8, but this time they didn't change the other term (3x)...