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\frac{\left(b+2c\right)\times 8c}{2\left(3b+6c\right)}
Divide \frac{b+2c}{2} by \frac{3b+6c}{8c} by multiplying \frac{b+2c}{2} by the reciprocal of \frac{3b+6c}{8c}.
\frac{4c\left(b+2c\right)}{3b+6c}
Cancel out 2 in both numerator and denominator.
\frac{4c\left(b+2c\right)}{3\left(b+2c\right)}
Factor the expressions that are not already factored.
\frac{4c}{3}
Cancel out b+2c in both numerator and denominator.
\frac{\left(b+2c\right)\times 8c}{2\left(3b+6c\right)}
Divide \frac{b+2c}{2} by \frac{3b+6c}{8c} by multiplying \frac{b+2c}{2} by the reciprocal of \frac{3b+6c}{8c}.
\frac{4c\left(b+2c\right)}{3b+6c}
Cancel out 2 in both numerator and denominator.
\frac{4c\left(b+2c\right)}{3\left(b+2c\right)}
Factor the expressions that are not already factored.
\frac{4c}{3}
Cancel out b+2c in both numerator and denominator.