Please find my answer below that how we could measure 15 min,

1. Start Both the hourglasses at a time.  (Both counting parallelly)
2.  11 min hourglass will complete first, once it has completed then reactive it (Like upper glass will be down) now  neck allows sand to go down.
3. Now, the 13 min hourglass still active and 11 min hourglass starts again from the beginning.
4. Once 13 min hourglass will be completed then rotate 11 min hourglass until sand get down (Note: This time 11 min hourglass only for 2 min)
This is the way we can measure the 15 min with both of the hourglasses.

1) start  both hourglasses
2) After 11 minutes turn the 11 hourglass upside down ()reactivate it)
3) After 13 minutes the 2nd hourglass finished so 2 minutes passed from the 11 hourglass
4) So now turn the 11 hourglass again upside down and it will finish after 2 minutes so we measured 15 minutes total