if i use Stare Down and target Kha'Zix, Evolving Hunter , will stare down use 4 might or 6 Might

It depends on Kha'Zix's Might when Stare Down resolves — and unless something has modified it, that number is 5, not 4 or 6.

Stare Down uses the chosen friendly unit's current Might and compares it to each enemy unit's current Might at resolution (Rule 710; units are always evaluated at their current Might unless a card says otherwise). Kha'Zix, Evolving Hunter is printed at 5 Might, so enemy units with Might 4 or less get moved to base — and if he's been buffed to 6 or shrunken to 4 by the time Stare Down resolves, that new value is what's compared.

The 4/6 numbers belong to Kha'Zix, Mutating Horror (4 base, 6 while the "alone" bonus applies) — his XP, Hunt, and attack trigger don't change his Might, so Evolving Hunter's value stays whatever is printed or modified on the board.