In how many ways can the letters of the word DELHI be arranged...

The word DELHI consists of $5$ letters: $3$ consonants (D, L, H)$and 2$ vowels (E, I).

The arrangement of letters in the word is Consonant-Vowel-Consonant-Consonant-Vowel.

Since the positions of vowels and consonants must remain unchanged, the consonants can only be placed in the $1$st, $3$rd, and $4$th positions, and the vowels can only be placed in the $2$nd and $5$th positions.

The $3$ consonants can be arranged in their $3$ positions in $3!$ ways.

The $2$ vowels can be arranged in their $2$ positions in $2!$ ways.

Total number of arrangements = $3! \times 2! = 6 \times 2 = 12$.

Answer: $12$