Saved from a previous post:

If you want exact matches for just two columns (and return a value from a
third), you could use:

=index(othersheet!$c$1:$c$100,
  match(1,(a2=othersheet!$a$1:$a$100)*(b2=othersheet!$b$1:$b$100),0))

(all in one cell)

This is an array formula.  Hit ctrl-shift-enter instead of enter.  If you do it
correctly, excel will wrap curly brackets {} around your formula.  (don't type
them yourself.)

Adjust the range to match--but you can't use the whole column.

This returns the value in othersheet column C when column A and B (of
othersheet) match A2 and B2 of the sheet with the formula.

And you can add more conditions by just adding more stuff to that product
portion of the formula:

=index(othersheet!$d$1:$d$100,
  match(1,(a2=othersheet!$a$1:$a$100)
         *(b2=othersheet!$b$1:$b$100)
         *(c2=othersheet!$c$1:$c$100),0))