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\frac{x+2}{\left(2x+4\right)\times 8}
Divide \frac{1}{2x+4} by \frac{8}{x+2} by multiplying \frac{1}{2x+4} by the reciprocal of \frac{8}{x+2}.
\frac{x+2}{2\times 8\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{1}{2\times 8}
Cancel out x+2 in both numerator and denominator.
\frac{1}{16}
Multiply 2 and 8 to get 16.