We can write this problem as:

#(4/9)/8# which can be rewritten as: #(4/9)/(8/1)#

We can then use this rule for dividing fractions to evaluate the expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#(color(red)(4)/color(blue)(9))/(color(green)(8)/color(purple)(1)) =>#

#(color(red)(4) xx color(purple)(1))/(color(blue)(9) xx color(green)(8)) =>#

#(cancel(color(red)(4))color(red)(1) xx color(purple)(1))/(color(blue)(9) xx cancel(color(green)(8)) color(green)(2)) =>#

#(color(red)(1) xx color(purple)(1))/(color(blue)(9) xx color(green)(2)) =>#

#1/18#