I got the answer and did not understand it,please explain the yellow highlight part.Thank you!

Give an expression in terms of functions assuming a rate of interest per month for the present value, 3 years before the first payment is made, of an annuity on which there are payments of $200 every 4 months for 12 years: Sia(4.1) a) Expressed as an annuity-immediate. b) Expressed as an annuity-due. akan(43) 6. (a) We use the technique developed in Section 3.4 that puts in imaginary payments and then subtracts them out, together with adapting formula (4.1), to obtain s7200(a176a32).why? Note that the number of payments is 417632=36, which checks. (b) Similar to part (a), but adapting formula (4.3) rather than (4.1), we obtain a41200(a180a36).why? Again we have the check that 418036=36