That is what the formula does, as I explained. If you want zero, change "" to 0.
When I copy-and-paste the formula as posted, I do not get any error.
As I mentioned, perhaps you need to use semicolon (";") instead of comma (",") between parameters, to wit:
=IF(AND(B3="dth"; F3="dth"); E3+I3; "")
Alternatively, perhaps E3 and/or I3 contains text that Excel does not interpret as numeric. Be sure that ISNUMBER(E3) and ISNUMBER(I3) return TRUE.
If you want the flexibility of E3 and/or I3 containing non-numeric text, use N(E3)+N(I3) instead of E3+I3.
Do those suggestions resolve the problem?