The Rule of 72 is a shortcut method to find the number of years to double your investment. This is only an estimation. This can be done by dividing 72 by the annual interest rate.
However, you are given a nominal rate since it is compounded annually. Let's convert this by this equation:
annual rate = (1+i/m)^m - 1, where m is the number of periods in a year. Thus, m=2
annual rate = (1 + 0.065/2)^2 -1 = 6.61%
Applying Rule of 72,
72 ÷ 6.61% = 10.89
This is where I found a problem. The answer here just directly divided 72 by 6.5% which will equal to 11.1 years. This is not accurate, since the given interest is compounded semi-annually. That is not an annual interest rate.
Nevertheless, the answer is still close to letter A.) 11.1 years.
