Answer:The coefficient is 15120. Step-by-step explanation:Since, by the binomial expansion formula,[tex](x+y)^n=\sum_{r=0}^n^nC_r x^{n-r} y^r[/tex]Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we can write,[tex](3x+2y)^7 = \sum_{r=0}^n ^7C_r (3x)^{7-r} (2y)^r[/tex]For finding the coefficient of [tex]x^3y^4[/tex],r = 4,So, the term that contains [tex]x^3y^4[/tex] = [tex]^7C_4 (3x)^3 (2y)^4[/tex][tex]=35 (27x^3) (16y^4)[/tex][tex]=15120 x^3 y^4[/tex]Hence, the coefficient of [tex]x^3y^4[/tex] is 15120.