a)

$\sqrt{18}\cdot \sqrt{2}=\sqrt{18\cdot 2}=\sqrt{36}=6$

b)

$\sqrt{18}:\sqrt{2}=\sqrt{9}=3$

c)

$\sqrt{\frac{3}{8}}\cdot \sqrt{\frac{3}{2}}=\sqrt{\frac{3}{8}\cdot \frac{3}{2}}=\sqrt{\frac{9}{16}}=\frac{\sqrt{9}}{\sqrt{16}}=\frac{3}{4}$

d)

$\sqrt{\frac{12}{7}}:\sqrt{\frac{7}{3}}=\sqrt{\frac{12}{7}:\frac{7}{3}}=\sqrt{\frac{12}{7}\cdot \frac{3}{7}}=\sqrt{\frac{36}{49}}=\frac{\sqrt{36}}{\sqrt{49}}=\frac{6}{7}$