Solution:

To find the number of matches in a double league tournament with 6 teams, we need to follow the below steps:

Step 1: Total number of matches played by a team in a double league tournament with n teams is (n-1).

Step 2: In a double league tournament, each team plays against every other team twice, once at home and once away.

Step 3: Hence, the total number of matches in a double league tournament with n teams can be calculated as:

Total number of matches = (n-1) * number of matches played by each team

Step 4: Number of matches played by each team in a double league tournament with n teams is:

Number of matches played by each team = (n-1) home matches + (n-1) away matches

Number of matches played by each team = 2 * (n-1)

Step 5: Substituting the value of number of matches played by each team in the above formula, we get:

Total number of matches = (n-1) * 2 * (n-1)

For n = 6, we get:

Total number of matches = (6-1) * 2 * (6-1) = 5 * 2 * 5 = 50

Step 6: However, this formula counts each match twice (once as a home match and once as an away match), so we need to divide the result by 2 to get the actual number of matches played.

Actual number of matches played = Total number of matches / 2

For n = 6, we get:

Actual number of matches played = 50 / 2 = 25

Hence, the correct answer is option 'D', i.e., 30.