2. \( \frac{6 t^{3} q^{2} \times 2 r^{3}}{3 t^{3} x r^{2}} \)

To simplify the expression \( \frac{6 t^{3} q^{2} \times 2 r^{3}}{3 t^{3} x r^{2}} \), we first multiply the numerators: \[ 6 t^{3} q^{2} \times 2 r^{3} = 12 t^{3} q^{2} r^{3} \] Now we can rewrite the whole expression as: \[ \frac{12 t^{3} q^{2} r^{3}}{3 t^{3} x r^{2}} \] Next, we can simplify the fraction by canceling out common terms. The \( t^{3} \) in the numerator and denominator cancels out, and we can also simplify the coefficients and the \( r^{3} \) over \( r^{2} \): \[ \frac{12}{3} = 4 \] And for the r terms: \[ \frac{r^{3}}{r^{2}} = r^{1} = r \] Putting it all together, we get: \[ \frac{4 q^{2} r}{x} \] Thus, the simplified expression is: \[ \frac{4 q^{2} r}{x} \]