How did they get to this answer can someone explain the steps.

Directions: Find the future value of each ordinary annuity, if payments are made and interest is compounded as given.

R = 15,000; 12.1% interest compounded quarterly for 6 yrs.

answer: $518,017.56

I assume R is the quarterly payment, "PYMT"
The number of periods is 6x4 = 24
The interest rate per period is
i = 12.1/4 = 3.025%

Future Value of Annuity
= PMT*[((1 + i)^n - 1) /i]

See http://www.getobjects.com/Components/Finance/TVM/fva.html for more details