Cryptic crossword clue
Supposes and hopes his stye gets treated 12

The most common and most likely answer to this crossword clue is the 12 letter word HYPOTHESISES

I've seen this crossword clue in The Daily Telegraph
H
Y
P
O
T
H
E
S
I
S
E
S

Buddy explains!

The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does HYPOTHESISES mean?

HYPOTHESISES verb
  1. To believe or assert on uncertain grounds.

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