APPLE = 1. Not the A from Auras, not the second p from tapes, not the L from tails. This leaves _ P _ _E.
SPITE = 2, not the i because of tails. SP_TE
WRITE = 3, not the i because of tails, so WR_TE
We need 2 letters from SP_TE and 3 from WR_TE. There is no way to have 3 letters frm WR_TE and not have a letter overlap with SP_TE. So either the t and/or the e is correct.
There is no way for the S and the P (together) to be correct in SP_TE because then we cannot get three correct letters from WR_TE. So, it's the S or P, or neither. If neither, the last letter is e for sure. If s, the last letter is still e for sure (eliminating the P from _ P _ _ E). If it's P, then the other letter must be T because because we cannot have P and E together (hence, only one from _ P _ _ E).
So, our possible combinations are ST, SE, and PT.
Now we much look at WR_TE. Our possible combinations are WRT, WRE, WTE, and RTE.
Anything with a leading S cannot match up with a leading W because they are in the same place.
So, our possibilities are: WRT+PT, WRE+PT, WTE+PT, RTE+ST, RTE+SE
R's and P's also cannot go together because they occupy the same place. So, now we have:
WTE+PT and RTE + SE, written out, in order, they are WP_TE and SR_TE
WP_TE is not possible because P and E cannot be together, leaving:
SR_TE
However, this is also not possible because that has 3 letters from SPITE. Which is why we must use the RTE by itself, because everything else has been logically eliminated.
Therefore:
_R_TE
(Lmao... I really hope I did that right. If I left out anything, it will screw everything up.. )