The time difference between both the hour glasses is 4 minutes and we should make use of this time and add it to 11 minutes hour glass time to get 15 minutes.

At time 0 minutes:

hour glass1 - 0-11

hour glass2 - 0-7

At time 7 minutes:

hour glass1 - 7-4

hour glass2 - 7-0

Invert hour glass2.

At time 11 minutes:

hour glass1 - 11-0

hour glass2 - 4-3

Again invert hour glass2 to make use of the 4 minutes difference.

At 15 minutes:

hour glass1 - 11-0

hour glass2 - 0-7

When hour glass2 is emptied 15 minutes would pass.