Mark had 24 newspapers to deliver. In one apartment building, he delivers 3/8 of them. In the next apartment building, he delivers 2/3 of the remaining amount. How many papers does he have left to deliver?

To find out how many newspapers Mark has left to deliver, we need to subtract the number of papers he delivered from the total number of papers he had.

First, Mark delivered 3/8 of the 24 newspapers in the first apartment building:

(3/8) * 24 = 9 papers.

The remaining number of papers Mark had after delivering in the first apartment building would be:

24 - 9 = 15 papers.

Next, Mark delivered 2/3 of the remaining 15 papers in the second apartment building:

(2/3) * 15 = 10 papers.

The number of papers Mark has left to deliver now is:

15 - 10 = 5 papers.

Therefore, Mark has 5 papers left to deliver.

In the first apartment, Mark delivers 24 * (3/8) = <<24*(3/8)=9>>9 newspapers.

He has 24 - 9 = <<24-9=15>>15 newspapers left.
Then he delivers 15 * (2/3) = <<15*(2/3)=10>>10 newspapers in the next apartment building.
So, Mark has 15 - 10 = <<15-10=5>>5 newspapers left to deliver. Answer: \boxed{5}.