Answer
$\color{blue}{\dfrac{m+6}{m+3}}$
Work Step by Step
Use the rule $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain:
$=\dfrac{m^2+3m+2}{m^2+5m+4} \cdot \dfrac{m^2+10m+24}{m^2+5m+6}$
Factor each polynomial, then cancel the common factors to obtain:
$\require{cancel}
\\=\dfrac{(m+1)(m+2)}{(m+1)(m+4)} \cdot \dfrac{(m+6)(m+4)}{(m+3)(m+2)}
\\=\dfrac{\cancel{(m+1)}\cancel{(m+2)}}{\cancel{(m+1)}\cancel{(m+4)}} \cdot \dfrac{(m+6)\cancel{(m+4)}}{(m+3)\cancel{(m+2)}}
\\=\color{blue}{\dfrac{m+6}{m+3}}$
