The total number of words that can be made by writing the letters of the word PARAMETER so that no vowel is in between two consonants is

Consonants $-$  P, R, M, T, R

Vowels $-$  A, A, E, E

1 unit $\to \text{A}\text{P R M T R A E E}$

As no vowel should be in between 2 consonants, that all the consonants as 1 unit.

Now $\left(4vowels+1unit\right)=5$ units can be arranged in $\frac{5!}{2!\times 2!}$  Ways 

5 consonants can be arranged among themselves in  $\frac{5!}{2!}$ ways. 

As the letters are repeated.

Total number of arrangements $=\frac{5!}{2!2!}\times \frac{5!}{2!}=1800$