Answer: Option B
There are 7 letters in the given word, out of which there are 3 vowels and 4 consonants.
Let us mark the positions to be filled up as follows:
$$\left( {\mathop {}\limits^1 } \right)\left( {\mathop {}\limits^2 } \right)\left( {\mathop {}\limits^3 } \right)\left( {\mathop {}\limits^4 } \right)\left( {\mathop {}\limits^5 } \right)\left( {\mathop {}\limits^6 } \right)\left( {\mathop {}\limits^7 } \right)$$
Now, 3 vowels can placed at any of the three places out of four marked 1, 3, 5, 7
Number of ways of arranging the vowels
$$\eqalign{
& = {}^4{P_3} \cr
& = \left( {4 \times 3 \times 2} \right) \cr
& = 24 \cr} $$
4 consonants at the remaining 4 positions may be arranged in $${}^4{P_4} = 4! = $$  
24 ways
Required number of ways = (24 × 24) = 576