The word FUDGE has 5 different letters.
When, the vowels UE are always together, they can be supposed to form one letter.
Then, we have to arrange the letters FDG(UE).
Now, 4 letters can be arranged in 4! = 24 ways.
The vowels (UE) can be arranged in 2!= 2 ways.
Required number of ways = (24 x 2)
= 48.