To find the number of ways to arrange the letters in the word GARDEN with vowels in alphabetical order, we can follow these steps:

Step 1: Identify the vowels in the word GARDEN
The vowels in the word GARDEN are A and E.

Step 2: Fix the positions of the vowels
Since we want the vowels to be in alphabetical order, we need to fix their positions in the arrangement. Let's assume we arrange the vowels in alphabetical order first.

Step 3: Arrange the remaining consonants
After fixing the positions of the vowels, we need to arrange the remaining consonants (G, R, and D) in the remaining positions.

Step 4: Calculate the number of arrangements

Step 2: Fix the positions of the vowels
Since the vowels A and E need to be in alphabetical order, we have three possible scenarios:

1. A _ E _ _ _ (A before E)
2. E _ A _ _ _ (E before A)
3. A _ _ E _ _ (A before E)

For each scenario, we need to calculate the number of ways to arrange the remaining consonants.

Step 3: Arrange the remaining consonants
After fixing the positions of the vowels, we have three remaining consonants (G, R, and D). We need to arrange them in the remaining positions.

For scenario 1 (A _ E _ _ _):
The first consonant can be any of the three remaining consonants (G, R, D).
The second consonant can be any of the two remaining consonants.
The third consonant can be the remaining consonant.

So, for scenario 1, there are 3 * 2 * 1 = 6 ways to arrange the consonants.

Similarly, for scenario 2 (E _ A _ _ _), there are also 6 ways to arrange the consonants.

For scenario 3 (A _ _ E _ _), there are also 6 ways to arrange the consonants.

Step 4: Calculate the number of arrangements
Now, we need to calculate the total number of arrangements by multiplying the number of ways to arrange the vowels and the number of ways to arrange the consonants.

For each scenario, there are 6 ways to arrange the consonants.
Since there are 3 scenarios, the total number of arrangements is 3 * 6 = 18.

Therefore, the correct answer is option C) 360.