Answer
$${\text{sixth term}} = - 3584{x^3}{y^5}$$
Work Step by Step
$$\eqalign{
& {\text{sixth term of }}{\left( {4x - y} \right)^8} \cr
& {\text{In the sixth term, }} - y{\text{ has an exponent of }}6 - 1,{\text{ or 5, while }}4x \cr
& {\text{has an exponent of 8}} - 5,{\text{ or 3}}{\text{.}} \cr
& \cr
& {\text{Using the }}k{\text{th Term of The Binomial Expansion}} \cr
& {\text{sixth term}} = C\left( {8,5} \right){\left( {4x} \right)^3}{\left( { - y} \right)^5} \cr
& {\text{sixth term}} = \frac{{8!}}{{3!5!}}\left( {64{x^3}} \right)\left( { - {y^5}} \right) \cr
& {\text{sixth term}} = 56\left( {64{x^3}} \right)\left( { - {y^5}} \right) \cr
& {\text{sixth term}} = - 3584{x^3}{y^5} \cr} $$
