Assuming you want me to clarify the last line, notice that
4(2k) can be written as
4⋅2⋅2k−1 If we multiply the 4 and 2 we get 8. We assumed f(k) was divisible by 8, and so 6f(k) is divisible by 8, and so is the last term, i.e we can then say that all the terms in f(k+1) are divisible by 8, so f(k+1) must be divisible by 8, assuming f(k) is divisible by 8.
Not sure how to make it more clear, and I don't want to write the whole working out, you should try it for yourself.