Solution:

Total effort required by 4 painters for 22 days = 4 × 22 = 88 man-days.

Initial effort by 4 painters for 2 days = 4 × 2 = 8 man-days.

Job still requires 88 − 8 = 80 man-days, and there are 20 painters available to do it.

Additional effort required by 20 painters for 80 man-days = 80 / 20 = 4 days.

Thus, 4 more days are required to complete the painting job.

Alternative Shorter Solution:

4 painters require 22 − 2 = 20 more days to complete the job.
Therefore, 4 + 16 = 20 painters will require 20 × 4 / 20 = 4 more days to complete the job.

Food for thought:

The number of days for the job is inversely proportional to the number of painters. So, is 'number of days × number of painters = constant'?

What assumptions were made to arrive at the solution?
Is something assumed about the output of the painters?