Combination and Permutation Question

Consider the letters of the word MONDAY. How many permutations of 4 different letters can be chosen if:
2 vowels cannot be together?

Not sure if my logic is correct:
Calculate all permutations (6P4) - No vowel Perms(4P2) * six ways 2 vowels can be together (=6).
This gives me 288 which is the correct answer.

Is this the only way to get the correct answer or is there any way to do this using positive logic?