What are the bits for this cache?
Assuming you meant to say "The machine has a word size of 4 bytes" (instead of "bits"), then yes you are correct - the log2 of the number of words in a line. Since there are 4 bytes per word, the bottom 2 address bits (addr[1 : 0]) are used to select which byte of a word, and then next bits after that (addr[log2(L)-1 : 2]) are to select which word in the line. This assumes line size is L bytes, not L bits (if L is in bits, then first divide L by 8).