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Twelve words put N first and C third, and half of them open NIC.
I takes the second box in six of the twelve, fifty percent, and A takes three. E, O and U manage one each, so the page is really two branches and three strays.
NICER, NICHE, NICKS, NICKY, NICOL and NICHT all sit on one stem. NICER and NICHE are the two you would reach for, and the rest turn narrow quickly.
NACHO and NACRE carry the A branch and both are reachable. NECKS is the lone E entry and the most common word on the page after NICER.
H fills the fourth box in five of the twelve and K takes four. Between them that is nine of the page, so the fourth box is the one worth testing.
E and S each close three of the twelve, and nothing else takes more than one. Nothing repeats a letter, so a visible double rules the pattern out immediately.
They sit in different branches and differ in three boxes. NECKS is the more common word and tests K in the fourth box.
The nape of the neck. It is the only word here with U in the second box, so it either wins or clears a branch.
Yes, it runs N, A, C, H, O. It is one of three words here with A in the second box.