chunghyu,
Welcome to the forum!
I'm not sure what your tables are called, but assuming the table in Sheet1 is Table1 and the table in Sheet2 is Table2, then in Sheet2, C2 and copied down:
=INDEX(Table1[Funding Source],MATCH(1,INDEX((Table1[Project ID]=Table2[[#This Row],[Project ID]])*(Table1[Project Name]=Table2[[#This Row],[Project Name]])*(Table1[Budget]=MAX(INDEX((Table1[Project ID]=Table2[[#This Row],[Project ID]])*(Table1[Project Name]=Table2[[#This Row],[Project Name]])*Table1[Budget],))),),0))
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