Can someone help me answer or explain how to answer questions about DNA coding capabilities?
4 bases (A T C G) leads to 4 possible value per bit of information, which then leads to the formula: 4^n (n being the number of base). For the first part of your question regarding how can you have so much information, it has to do with n, as you increase the number of bases the number of different combinations increases exponentially. For a comparison, your computer stores information in a 2 value bit system (1 or 0).

If you plot the number of possibilities, you will see that DNA outpace computers very quickly, as an exponential of base 4 will go faster (2*2 = 4, 4*4 = 16, already at 2 bits you have 4 times as many possibilities)



With that in mind, you can compute the number of possibilities for any given number of bits (or bases in your case).