$$\frac{4}{6}:x=\frac{6}{11}:\frac{42}{55}$$
$x=\frac{14}{15}\approx 0.933333333$
$$\frac{4}{6}=x\times \frac{\frac{6}{11}}{\frac{42}{55}}$$
$$\frac{2}{3}=x\times \frac{\frac{6}{11}}{\frac{42}{55}}$$
$$\frac{2}{3}=x\times \frac{6}{11}\times \frac{55}{42}$$
$$\frac{2}{3}=x\times \frac{6\times 55}{11\times 42}$$
$$\frac{2}{3}=x\times \frac{330}{462}$$
$$\frac{2}{3}=x\times \frac{5}{7}$$
$$x\times \frac{5}{7}=\frac{2}{3}$$
$$x=\frac{2}{3}\times \frac{7}{5}$$
$$x=\frac{2\times 7}{3\times 5}$$
$$x=\frac{14}{15}$$
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