Answer
$${\text{eighth term}} = 90720{x^{28}}{y^{12}}$$
Work Step by Step
$$\eqalign{
& {\text{The middle term of }}{\left( {3{x^7} + 2{y^3}} \right)^8} \cr
& {\text{The binomial has 9 terms, then the middle term is the fifth}} \cr
& {\text{In the fifth term, }}2{y^3}{\text{ has an exponent of 5}} - 1,{\text{ or 4, while }}3{x^7} \cr
& {\text{has an exponent of 8}} - 4,{\text{ or 4}}{\text{.}} \cr
& \cr
& {\text{Using the }}k{\text{th Term of The Binomial Expansion}} \cr
& {\text{eighth term}} = \left( {8{\bf{C}}4} \right){\left( {3{x^7}} \right)^4}{\left( {2{y^3}} \right)^4} \cr
& {\text{eighth term}} = \frac{{8!}}{{4!4!}}\left( {81{x^{28}}} \right)\left( {16{y^{12}}} \right) \cr
& {\text{eighth term}} = 70\left( {81{x^{28}}} \right)\left( {16{y^{12}}} \right) \cr
& {\text{eighth term}} = 90720{x^{28}}{y^{12}} \cr} $$
