It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    


where  FV is the future value of the account;  P is the monthly payment (deposit); r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for for the monthly payment 


    P = .     (1)


Under the given conditions, FV = $24,000;  r = 0.046/12;  n = 20*12.  So, according to the formula (1), you get for the monthly payment 


    P =  = $61.14.


Answer.  The necessary monthly deposit value is $61.14.


Note that of projected $24,000 the total of deposits will be only  20*12 times $61.14, i.e. 20*12*61.14 = 14673.60 dollars.
The rest is what the account will earn/accumulate in 20 years.