\[\boxed{\text{636.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[b_{2} = b_{1} \cdot q = 6,\ \ b_{4} = b_{1} \cdot q^{3} = 24,\ \ \frac{b_{1}q^{3}}{b_{1}q} = \frac{24}{6};\ \]
\[q^{2} = 4,\ \ q = \pm 2;\]
\[1)\ q = 2,\ \ b_{1} = \frac{b_{2}}{q} = 3;\]
\[b_{6} = b_{1} \cdot q^{5} = 3 \cdot 2^{5} = 96;\]
\[2)\ q = - 2,\ \ b_{1} = \frac{b_{2}}{q} = - 3;\ \ \ b_{6} = b_{1} \cdot q^{5} = - 96.\]