MOTIVATION



There is only one repeated consonant, and that is the letter T



The vowels are {O,I,A,I,O}

The remaining consonants are {M,V,N}



The vowels can be arranged -- while staying together in one group -- in  5!/(2!*2!) ways or  120/(2*2) = 30 ways



The consonants {M,V,N} can be arranged in 3! = 6 ways

 

Finally, for EACH of these vowel AND consonant arrangements, there are 4 places to put the grouped vowels: 



    T,{vowels},{M,V,N},T

    T,M,{vowels},{V,N},T

    T,V,{vowels},{M,N},T

     etc.



This results in  30 * 6 * 4 =  ways to arrange the letters and satisfy the problem statement. 

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