Question 1120433
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I will assume "order matters" means the 6 different songs, and not just 4 rap and 2 country songs.  In that case, the 6 songs can be arranged in 6!=720 different orders.<br>
Then the number of ways you can choose 4 of the 23 rap songs is 23C4 = 8855 and the number of ways you can choose 2 of the 14 country songs is 14C2 = 91.<br>
The total number of ordered playlists is then<br>
720*8855*91 = 580179600