I can't help noticing that if this was a base 10 alphametic, then POISON is not possible, because that solution requires 12 letters, ABCEHILNOPST. All other choices require 9 or 10 letters, which is possible.

Also, if TO times I equals a three digit number, then TO times IN cannot be a six digit number, so it can't be POISON.

In fact, it can't be TOOL (because that requires IN to be greater than 100) and it can't be TABLE (because that requires IN to be a lot greater than 100).

So, the answer must be BAT or HINT.

/***********************************/

Except,

If TE times TILE = CLOTH, then C must be greater than T.

And if TA times I = CAB, then C must be less than T.

So we have a contradiction, and this is not an alphametic in any base. So it must be a trick! I guess Charlie is right again!