It takes 45 minutes for 4 people to paint 5 walls . how many minutes does it take 6 people to paint 4 walls?

It takes 45 * 4 = 180 people-minutes to paint 5 walls.
Therefore to paint 4 walls it will take:

The time needed for 6 people to paint 4 walls is given by 144/6 = 24 minutes.

Basically, because of the first part of your question, it takes 9 minutes for one person to paint a quarter of a wall. This means that it would take 36 minutes for one person to paint an entire wall. It also means that it would take 6 minutes for one person to paint 1/6 of a wall.

If there are 4 walls to paint, and 6 people around to paint them, each person would get 4/6 of a wall to paint. This means that it would take 24 minutes for these 6 people, working together, to paint 4 walls. 4 x 6 minutes (because they'd each be painting 4 x 1/6 of a wall) = 24 minutes.