sumif with 2 ranges and multiple criteria

[AC]

I need help figuring out how to sum a range if I have multiple criteria in 2
separate columns not next to one another. This is what I have but it's not
working:

sumif('ALC 2007 Q4'!I4:I346 or 'ALC 2007 Q4'!C4:C346, "Industry-all" or
"product 1" or "product 2", 'ALC 2007 Q4'!F4:F346)

 

[Teethless mama]

=SUMPRODUCT(('ALC 2007 Q4'!I4:I346={"Industry-all","Product 1","Product
2"})*'ALC 2007 Q4'!F4:F346)

 

[T. Valko]

If a criteria is in both ranges should it calculate as 2x or 1x. For
example:

C4 = Industry-all
I4 = product 2
F4 = 10

Should the result be 10 or 20?