Is the answer 22?

m + n + q = 30
also n = m + 6, therefore 2m + 6 + q = 30
2m + q = 24

For q to be the maximum, m has to be minimum. Assume m = 1, therefore q = 24 - 2 = 22

If not specified in the question can we consider the integers in the order m,n,q?

You have obviously assumed they are in that order as you have taken the median as n=m+6.

Obviously ! Its perfect to assume in this order . Among m , n and q based on given conditions , you know m cant be greatest as you have a median greater than m . So median could be q or n then . But since you are asked the greatest value of q , so q will be greatest only if its the biggest of the lot . Hence its logical to take q as the third one in this series to get the answer

Otherwise this question cannot be solved...

sanjana wrote:If not specified in the question can we consider the integers in the order m,n,q?

You have obviously assumed they are in that order as you have taken the median as n=m+6.