Unsurprisingly most here got 6/6, but what interests me is the different methods everyone used for number 6.
The Law of 72 is the easiest and most frequently used and gave the correct answer in this case, but is an approximation and can get you in trouble if you're near the boundary between one year and another for doubling time. Specifically with 20% interest the law of 72 gives a 3.6 year doubling time while the actual number is 3.8. Close enough in this case, but illustrates why some other posters were wise to double check with other methods.
The binomial expansion to several orders and the direct method of just calculating the compound each year certainly work, but require a good number of arithmetic calculations. While I could manage this, as I've gotten older my "internal stack height" of numbers I can hold in my head for calculations has gotten smaller (or I've just gotten lazier) and those seemed a bit laborious. I just squared 1.2 to get 1.44, saw that was more than sqrt(2) and that meant 1.2^4 > 2 hence the doubling time was less than 4 years. None of these methods is better or worse than any other, but its interesting to see how different heads work.
