Verified answer

[tex]\displaystyle \frac{32b^5}{15x^6}:\frac{4b^3}{45x^4}=\frac{32b^5}{15x^6}*\frac{45x^4}{4b^3}=\frac{8b^2}{x^2}*3=\frac{24b^2}{x^2}[/tex]