Please help, thank YOU if you try :)

c =  3 log _y^2 b^3

d = 2 log _y^3 b^2

Using the change of base  theorem

d =  2 [ log b^2 ] / [ log y^3 ]  =  [ 2* 2 log b ] / [ 3 log y]

c =  3 [ log b^3] / [ log y^2]  = [ 3*3  log b ] [ 2 log y]

d / c =   (4 log b) / ( 3 log y)              4 log b * 2 log y             

            _________________  =   ________________   =    8 / 27

              (9 log b) / ( 2 log y)            9 log b * 3 log y 

thanks!