(2x+3)^7 ..

so the coefficient of x^4 is

(7 C 4) (2x)^4 3^(3)

15120?

Ehh, yeah, but only by luck:

x^7, x^6, x^5,

**x^4**x^4 is the 4th term, which means we're looking at column 4, so r+1=4 => r=3.

7C3 is what you needed, but 7C4 = 7C3 because of the identity: nCk = nC(n-k)

Try again if I had asked for the x^5 term?