We can rewrite this problem as:
#((21b^3)/(4c^2))/(7/(6c^2))#
We can now use this rule for dividing fractions to find the quotient:
#(color(red)(a)/color(blue)(b))/(color(orange)(c)/color(purple)(d)) = (color(red)(a)xxcolor(purple)(d))/(color(blue)(b) xx color(orange)(c))#
#(color(red)(21b^3)/color(blue)(4c^2))/(color(orange)(7)/color(purple)(6c^2)) = (color(red)(21b^3)xxcolor(purple)(6c^2))/(color(blue)(4c^2) xx color(orange)(7)) = (126b^3c^2)/(28c^2) = (126b^3color(red)(cancel(color(black)(c^2))))/(28color(red)(cancel(color(black)(c^2)))) = ((14 xx 9)b^3)/(14 xx 2) =#
#((color(red)(cancel(color(black)(14))) xx 9)b^3)/(color(red)(cancel(color(black)(14))) xx 2) = (9b^3)/2# or #4.5b^3#
