The tricky part is in this requirement:
You need to ensure that database remains available if a catastrophic
server failure or a disk failure occurs. You need to maintain
transactional consistency of the data across both servers. You need to
achieve these goals without manual intervention.
The disk failure part means a failover cluster alone won't work because the storage is shared with both nodes. If the storage where the data files live fails, then both nodes will be affected.
However, a 2-node synchronous Availability Group isn't the answer either, because as Microsoft's own documentation points out:
If primary's session-timeout period is exceeded by a secondary replica, the primary replica temporarily shifts into asynchronous-commit mode for that secondary replica. When the secondary replica reconnects with the primary replica, they resume synchronous-commit mode.
Read further in that link in the "Factors That Disrupt Data Synchronization" section, and Microsoft elaborates on the reasons why you can't guarantee that a 2-node AG will not lose data on failover.
So what's the right answer for SQL Server 2012?
There isn't one. You can't guarantee zero data loss with 2 independent SQL Server 2012s without third party tools (like SAN replication, and even then, there's a ton of work involved.) I'm guessing the question came from a test or certification written by somebody without real-world experience. That wouldn't be the first time, and it won't be the last.
Is there a right answer for later versions?
Yes, SQL Server 2017 introduced a new REQUIRED_SYNCHRONIZED_SECONDARIES_TO_COMMIT setting at the Availability Group level. The default is 0, which means as long as the primary receives the transaction, it's committed. You can change that to 1 (or more), which means that if at least that number of secondaries don't also commit the transaction, then the transaction fails.