What is the result of multiplying 12/8 by 6/9 by 24/2?

First, simplify $\frac{12}{8}$ by dividing both numerator and denominator by 4, resulting in $\frac{3}{2}$.

$$\frac{3}{2} \times \frac{6}{9} \times \frac{24}{2}$$

Next, simplify $\frac{6}{9}$ by dividing both numerator and denominator by 3, resulting in $\frac{2}{3}$.

$$\frac{3}{2} \times \frac{2}{3} \times \frac{24}{2}$$

Now, we can cross-cancel:

• The 3 in the numerator of the first fraction with the 3 in the denominator of the second fraction.
• The 2 in the numerator of the second fraction with the 2 in the denominator of the first fraction.

$$\frac{3^{\div 3}}{2^{\div 2}} \times \frac{2^{\div 2}}{3^{\div 3}} \times \frac{24}{2} = \frac{1}{1} \times \frac{1}{1} \times \frac{24}{2}$$

Finally, simplify $\frac{24}{2}$ by dividing both numerator and denominator by 2, resulting in $\frac{12}{1}$.

$$\frac{1}{1} \times \frac{1}{1} \times \frac{12}{1}$$

$$\frac{1 \times 1 \times 12}{1 \times 1 \times 1} = \frac{12}{1} = 12$$

The final answer is $\text{12}$.