Multiply the following fractions: 6/4 14/2 12/6

First, simplify 6 (numerator of the first fraction) and 6 (denominator of the third fraction) by dividing both by 6:

$$\frac{6^{\div 6}}{4} \times \frac{14}{2} \times \frac{12}{6^{\div 6}} = \frac{1}{4} \times \frac{14}{2} \times \frac{12}{1}$$

Next, simplify 14 (numerator of the second fraction) and 2 (denominator of the second fraction) by dividing both by 2:

$$\frac{1}{4} \times \frac{14^{\div 2}}{2^{\div 2}} \times \frac{12}{1} = \frac{1}{4} \times \frac{7}{1} \times \frac{12}{1}$$

Finally, simplify 12 (numerator of the third fraction) and 4 (denominator of the first fraction) by dividing both by 4:

$$\frac{1}{4^{\div 4}} \times \frac{7}{1} \times \frac{12^{\div 4}}{1} = \frac{1}{1} \times \frac{7}{1} \times \frac{3}{1}$$

$$\frac{1 \times 7 \times 3}{1 \times 1 \times 1} = \frac{21}{1} = 21$$

The final answer is $\text{21}$.