There are a few things wrong here. First, the formula t = i/pr works for simple interest only, not compound interest. And second, the denominator of that should be the amount invested, which was 175K. So that formula would yield t = 75/(175*.06) = 7.14, meaning it would take 7.14 years of simple interest to make the investment reach $250K.
For compound interest you use: where i is the interest rate per period and n is the number of periods of time. In this case a period is half a year in duration, and so the value for i is 0.06/2. PV is the present (or beginning) value and FV is the future (or ending) value. So you have:
Do you know how to solve for n? Hint - it requires using logarithms. Once you have a value for n, round up to the next whole number and then multiply by 6 to get the number of months.