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Nineteen words put X second and I third, and the AXI and EXI families carry most of the page.
AXIAL, AXILE, AXILS, AXIOM and AXION all trace back to axis or the Greek axioma. A opens seven of the nineteen, more than any other letter.
EXIST, OXIDE, EXILE, EXITS and AXIAL are the entries in general use. AXIOM and OXIME come up in mathematics and chemistry.
It is the only entry here that opens with X, and it is not English vocabulary. Word lists picked it up from spelling dictionaries, which record numerals alongside words.
Treat the page as holding one fewer real option. No setter would use a numeral as an answer, and you could not reason towards it if they did.
E and S each close six of the nineteen, which is most of the page between them. The E ending comes from EXILE, OXIDE, AXILE, AXITE and EXINE.
The fourth box is the scattered one, with ten letters appearing across nineteen words and nothing above three.
So the opening letter and the ending do the work here. Once you know whether the word begins A, E or O, and whether it ends E or S, very little is left.
OXIDE tests the O and D and covers the E ending. EXIST doubles nothing but its letters overlap heavily with EXILE and EXITS.
A hypothetical elementary particle proposed in physics. AXIOM, a self evident truth, sits one letter away and is far commoner.
The tough outer coat of a pollen grain, a botany term and one of the more obscure entries here.
South African flowering plants of the iris family. It is the one entry that opens with I.