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$1)\; \; \left (\sqrt{74\frac{2}{3}}-\sqrt{4\frac{2}{3}}\right ):\sqrt{\frac{14}{27}}=\left (\sqrt\frac{224}{3}}-\sqrt{\frac{14}{3}}\right ):\sqrt{\frac{14}{27}}=\\\\=\frac{\sqrt{16\cdot 14}-\sqrt{14}}{\sqrt3}:\sqrt{\frac{14}{27}}=\frac{\sqrt{14}(\sqrt{16}-1)}{\sqrt3}\cdot \sqrt{\frac{27}{14}}=\\\\=\frac{\sqrt{14}(4-1)}{\sqrt3}\cdot \frac{\sqrt{27}}{\sqrt{14}}=\frac{3\cdot 3\sqrt3}{\sqrt3}=9$

$2)\; \; \frac{12}{13}\sqrt{6\frac{1}{2}}:\sqrt{1\frac{5}{13}}= \frac{12}{13} \sqrt{\frac{13}{2}}:\sqrt{\frac{18}{13}}=\frac{12\cdot \sqrt{13}\cdot \sqrt{13}}{13\cdot \sqrt2\cdot \sqrt{9\cdot 2}}=\\\\=\frac{12}{\sqrt2\cdot 3\sqrt2}=\frac{6}{3}=2$