$$\frac{2}{3}:x=\frac{6}{11}:\frac{11}{6}$$
$x = \frac{121}{54} = 2\frac{13}{54} \approx 2.240740741$
$$\frac{2}{3}=x\times \frac{\frac{6}{11}}{\frac{11}{6}}$$
$$\frac{2}{3}=x\times \frac{6}{11}\times \frac{6}{11}$$
$$\frac{2}{3}=x\times \frac{6\times 6}{11\times 11}$$
$$\frac{2}{3}=x\times \frac{36}{121}$$
$$x\times \frac{36}{121}=\frac{2}{3}$$
$$x=\frac{2}{3}\times \frac{121}{36}$$
$$x=\frac{2\times 121}{3\times 36}$$
$$x=\frac{242}{108}$$
$$x=\frac{121}{54}$$
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