In the word 'MATHAEMATICS' there are 7 consonants which are M-2 ,,H-1,C-1,S-1, T-2 .Since they have to occur together we treat them as a single unit.
Now this single unit together with the remaining 4 vowels which are A-2,E-1,and I-1 will account for 5 letters.
Now in these 5 letters we have A is repeating twice these can be aarranged in different ways.
Corresponding to each of these arrangements the consonents can be arranged in different ways.
Hence the number of ways it can be arranged is =75600