The expression is:

$$
\(\frac{\frac{4}{5} \times 10 \times \frac{3}{4} \times 12}{\frac{3}{10} \times 5 \times \frac{7}{8} \times 24}\)
$$


First, let's simplify the numerator:

$$
\(\text { Numerator }=\frac{4}{5} \times 10 \times \frac{3}{4} \times 12\)
$$


We can rearrange and cancel out terms to make it easier:

$$
\(\begin{gathered}
\text { Numerator }=\left(\frac{4}{5} \times 10\right) \times\left(\frac{3}{4} \times 12\right) \\
\text { Numerator }=(4 \times 2) \times(3 \times 3) \\
\text { Numerator }=8 \times 9=72
\end{gathered}\)
$$


Now, let's simplify the denominator:

$$
\(\text { Denominator }=\frac{3}{10} \times 5 \times \frac{7}{8} \times 24\)
$$


Rearrange and simplify:

$$
\(\text { Denominator }=\left(\frac{3}{10} \times 5\right) \times\left(\frac{7}{8} \times 24\right)\)
$$

$$
\(\begin{gathered}
\text { Denominator }=\left(\frac{3 \times 5}{10}\right) \times\left(\frac{7 \times 24}{8}\right) \\
\text { Denominator }=\left(\frac{15}{10}\right) \times(7 \times 3) \\
\text { Denominator }=\left(\frac{3}{2}\right) \times 21 \\
\text { Denominator }=\frac{63}{2}
\end{gathered}\)
$$


Finally, divide the numerator by the denominator:

$$
\(\text { Final Answer }=\frac{72}{\frac{63}{2}}\)
$$


To divide by a fraction, you multiply by its reciprocal:

$$
\(\text { Final Answer }=72 \times \frac{2}{63}\)
$$


Now, simplify the expression. Both 72 and 63 are divisible by 9 .

$$
\(\begin{gathered}
\text { Final Answer }=(8 \times 9) \times \frac{2}{(7 \times 9)} \\
\text { Final Answer }=8 \times \frac{2}{7}=\frac{16}{7}
\end{gathered}\)
$$

Now, convert the improper fraction to a mixed number:

$\(\frac{16}{7}=2\)$ with a remainder of 2

So, the final answer is $\(2 \frac{2}{7}\)$.

This corresponds to option (B).