Final answer:
The prefix-length for the IPv6 address range 2001:0db8:bc15:00a0:0000:: to 2001:0db8:bc15:00af:0000:: is /60, as the addresses differ only in the last 4 bits of the fourth hextet.
Step-by-step explanation:
The student is asking about the prefix-length for a given range of IPv6 addresses, specifically between 2001:0db8:bc15:00a0:0000:: and 2001:0db8:bc15:00af:0000::. To determine the prefix-length, we need to find the common prefix bits of the range.
In this case, the addresses differ only in the fourth hextet where one starts with 00a0 and the other ends with 00af. Since the addresses are the same up until the final hexadecimal digit of this hextet, we need to find out how many bits are consistent across all addresses in the range.
Converting 00a0 to binary gives us 0000 0000 1010 0000 and 00af to binary is 0000 0000 1010 1111. Noticing that the first 52 bits are the same, we ascertain that the varying part starts from the 53rd bit, thereby giving us a prefix-length of /52.
However, since the question does not offer /52 as an option and the addresses differ only in the last 4 bits of the fourth hextet, which corresponds to 16 bits (4 hexadecimal digits = 16 bits), we can say that the subnet mask covers the first 60 bits, leaving the last 4 bits as the allowance for address variations within that subnet; thus, the prefix-length is /60.