The difficult part here is to separate multi-column ranges into separate rows - one way to do that is with OFFSET
within COUNTIF
, i.e. this formula
=SUMPRODUCT(COUNTIF(OFFSET($B$2:$D$6,ROW($B$2:$D$6)-ROW($B$2),0,1),$A2),COUNTIF(OFFSET($E$2:$H$6,ROW($E$2:$H$6)-ROW($E$2),0,1),B$1))
That assumes that all suitors are different on any one row and all opponents are different on any one row (although formula can be modified if that isn't the case).
You can extend the ranges to any size you want - although the number of rows must be the same for each part
....or here's another more obscure way using MMULT
function
=SUMPRODUCT(MMULT(($B$2:$D$6=$A2)+0,{1;1;1}),MMULT(($E$2:$H$6=B$1)+0,{1;1;1;1}))
the {1;1;1} and {1;1;1;1} represent the number of columns in each section so if you have 6 and 8 those need to be changed accordingly