How many different ways the letter can be formed Hindustan so that all the vowels never come together?

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I went on to proceed with this problem by subtracting the number of arrangements in which all vowels were together, from the total number of arrangement which proved time consuming. An alternative solution, given by the textbook was what they called the gap method.

They find the number of ways of arranging $6$ consonants. "Then they say that there are $7$ gaps remaining (how!!!!!)" in which the remaining $6$ vowels are arranged in $\frac{7p6}{3!2!}$. The answer is $151200$