Here's an addendum to this :
Let a = m and [ 2b + 3c] = n
So we are looking for the term in (m + n)^6 where a = m has a power of 1....and this is given by
C(6,1) mn^5 = 6an^5
So....we have
6a [ 2b + 3c]^5
And now we are looking for the term in (2b + 3c)^5 where [2b] has a power of 2....and this is given by:
C(5, 2) [2b]^2 [3b]^3 = 10 * 4b^2 * 27c^3 = 1080 b^2 c^3
Putting this all together, the term we are looking for is given by
6a [ 1080 b^2 c^3] = 6480ab^2c^3 ....... and 6480 is the coefficient
