The typical question is to describe all x's such that

x = 11 mod (39), and

x = 7 mod (22)

Since 22 and 39 are relatively prime, you can find the following 2 relations:

22*16 = 1 mod 39, and

39*13 = 1 mod 22.

Then you make the number:

n = 11*22*16 + 7*39*13 + k * 22 * 39, with k an arbitrary integer

Note that:

n = 11 mod 39, and

n = 7 mod 22

so this satisfies what you're looking for.

Now:

n = 7421 + k*22*39, or

n = 7421 mod (22*39), or

n = 557 mod 858.