Answer
$n=\frac{2}{21}$
Work Step by Step
$\frac{\frac{7}{9}}{\frac{8}{27}}=\frac{\frac{1}{4}}{n}$ $\longrightarrow$ cross multiply to solve for n
$\frac{7}{9}n=\frac{8}{27}\times\frac{1}{4}$$\longrightarrow$multiply
$\frac{7}{9}n=\frac{8}{108}$$\longrightarrow$multiplication property of equality
$\frac{7}{9}n\times\frac{9}{7}=\frac{8}{108}\times\frac{9}{7}$$\longrightarrow$ multiply
$n=\frac{72}{756}$$\longrightarrow$simplify
$n=\frac{72\div36}{756\div36}$
$n=\frac{2}{21}$