Treat the vowels like they are 1 block, as if they are one letter. But in this vowel block there are 4 vowels, 2 of which are the same. The number of ways of arranging these 4 vowels is then <span><span><span>4!</span><span>2!</span></span><span><span>4!</span><span>2!</span></span></span>.
Now, treating this block aa one letter, we have 7 consonants and 1 block, so there are 8 'letters' to arrange with two M's and two T's. So we have to divide out by 2! for each. So we get: <span><span><span>8!</span><span>2!2!</span></span><span><span>8!</span><span>2!2!</span></span></span>.
Finally we multiply this by the number of ways the vowels can be arranged to get:
<span><span><span>4!</span><span>2!</span></span><span><span>8!</span><span>2!2!</span></span></span>
