In cell C11:
=MAX(INDEX(B3:K6,MATCH(C9,A3:A6,0),0))
In cell D11:
=INDEX(A2:K2,MAX(IF(INDEX(B3:K6,MATCH(C9,A3:A6,0),0)=C11,COLUMN(B2:K2))))
or better, especially if your dates aren't sorted left to right:
=MAX(IF(INDEX(B3:K6,MATCH(C9,A3:A6,0),0)=C11,B2:K2))
These last two formulae may need to be entered with Ctrl+Shift+Enter, not just plain Enter, depending on your version of Excel.