You have $500,000 available to invest. The risk-free rate as well as
your borrowing rate is 8%. The return on the risky porfolio is 16%. I
f you wish to earn a 22% return, you should_________?

a)invest 125,000 in the risk free asset
b)invest 375,000 in the risk free asset
c)borrow 125,000
d)borrow 375,000

the answer is d, but I need the explanation and procedures.

It's simple maths - 

500,000 original
375,000 borrowed

Return in risky portfolio = 140,000 (875,000 @ 16%)
Interest cost =              30,000
Return on 500,000 =         110,000

110,000 = 22% of 500,000

This is, of course, a very very risky way of investing as the money is
"geared", your positive return is magnified but so is the negative.

Hope this helps and I trust this isn't homework!