Originally Posted by xor

Alternative (but hardly any better) formula:

=SUMPRODUCT(($G$2:$G$1000="Groups 3rd")+($G$2:$G$1000="FTI 3rd"),$F$2:$F$1000)

SUMIFS cannot handle OR-conditions.

Please be aware that you should never use full column references (as G:G) i array- or array-like formulas (like SUMPRODUCT), but adjust the range to what is needed.