The number of even proper divisors of 1008 is

_{$1008=2^4\times 3^2\times 7$}  

_$\therefore$ the required number of even proper divisors = total number of selections of at least one 2 and any number of 3’s or 7’s _{$=4\times \left(2+1\right)\times \left(1+1\right)-1=23.$}