If SHA256 produces an alphanumeric hash, how can a hash be "less than a certain value"?
Not that other answers are wrong here, but just to approach your confusion from another angle:


  SHA256 hashing algorithm, which produces alphanumeric hashes.


That's not true. The hashing algorithm produces a stream of bytes. Only when you display that bunch of bytes on your screen it's common for it to be in hexadecimal (containing "alphanumeric" characters A to F) but that's just for display purposes to make it human-readable.

You may as well display that same bytes as a large decimal number (requires more screen space and doesn't have the advantage that each two digits represent exactly one byte from the original. Or you could display it in binary: 256 zeroes and ones.


  My question is, how can one alphanumeric hash output be "less than" another?


Even disregarding the above, what stops you from sorting a list of words alphabetically? One word will be "less than" another word.