BASIS
if 2 then I is the fourth.
From BAITS - 1,the known A, so not B or the second S; and from HASTE - 1, again the known A, so not the first S.
if 1 then B is the third and C is last.
From HABIT - 2, the known A and not H from HASTE - 1, not the I from BASIS - 1, and not the T from YACHT - 1.
And from BASIC - 2, not the BASI.