Решение:

1. $$\frac{6}{25} \cdot \frac{5}{12} = \frac{6 \cdot 5}{25 \cdot 12} = \frac{30}{300} = \frac{1}{10}$$
2. $$\frac{15}{22} \cdot \frac{11}{20} = \frac{15 \cdot 11}{22 \cdot 20} = \frac{165}{440} = \frac{3 \cdot 5 \cdot 11}{4 \cdot 5 \cdot 11 \cdot 2} = \frac{3}{8}$$
3. $$\frac{7}{4} \cdot \frac{12}{35} = \frac{7 \cdot 12}{4 \cdot 35} = \frac{84}{140} = \frac{7 \cdot 12}{4 \cdot 7 \cdot 5} = \frac{12}{20} = \frac{3 \cdot 4}{5 \cdot 4} = \frac{3}{5}$$
4. $$\frac{18}{5} \cdot \frac{40}{9} = \frac{18 \cdot 40}{5 \cdot 9} = \frac{720}{45} = 16$$
5. $$\frac{3}{a} \cdot \frac{2a}{15} = \frac{3 \cdot 2a}{a \cdot 15} = \frac{6a}{15a} = \frac{2 \cdot 3 \cdot a}{5 \cdot 3 \cdot a} = \frac{2}{5}$$
6. $$\frac{9c}{8} \cdot \frac{56}{3c} = \frac{9c \cdot 56}{8 \cdot 3c} = \frac{504c}{24c} = 21$$
7. $$\frac{1}{13b} \cdot \frac{26}{3} = \frac{1 \cdot 26}{13b \cdot 3} = \frac{26}{39b} = \frac{2}{3b}$$
8. $$\frac{4k}{9} \cdot \frac{27}{20} = \frac{4k \cdot 27}{9 \cdot 20} = \frac{108k}{180} = \frac{3k}{5}$$
9. $$\frac{1}{a-b} \cdot \frac{1}{a+b} = \frac{1 \cdot 1}{(a-b) \cdot (a+b)} = \frac{1}{a^2 - b^2}$$
10. $$\frac{1}{2(c-3)} \cdot \frac{1}{(c-3)} = \frac{1 \cdot 1}{2(c-3) \cdot (c-3)} = \frac{1}{2(c-3)^2}$$
11. $$\frac{3+c}{4} \cdot \frac{9}{2(3+c)} = \frac{(3+c) \cdot 9}{4 \cdot 2(3+c)} = \frac{9}{8}$$
12. $$\frac{5(x+y)}{63} \cdot \frac{7}{3(x+y)} = \frac{5(x+y) \cdot 7}{63 \cdot 3(x+y)} = \frac{35(x+y)}{189(x+y)} = \frac{5}{27}$$