Answer: $18$

Explanation:$1$. Simplify the given expression $(6x^{2})(3x^{7})$: Multiply the constant coefficients: $6 \times 3 = 18$ Multiply the variable parts using the exponent rule $x^m \cdot x^n = x^{m+n}$: $x^{2} \cdot x^{7} = x^{2+7} = x^{9}$

$2$. Combine the results: $(6x^{2})(3x^{7}) = 18x^{9}$

$3$. Compare the simplified expression with $bx^{9}$: We have $18x^{9}$ is equivalent to $bx^{9}$. By comparing the coefficients of $x^9$, we find that $b = 18$.

$4$. Conclusion: The value of b is $18$.