VLookup/Index/Columns to rows

First, you'll need to insert a new column in Sheet2, Column C where C2 =A2&B2, dragged down. You can hide that column if you like.

Next, some of your names on Sheet1 col A have spaces after them. Get rid of them or you won't get matches.

In Sheet1!B2, dragged across and down

=INDEX(Sheet2!$D$2:$G$13,MATCH($A2&LEFT(B$1,4),Sheet2!$C$2:$C$13,0),MATCH(RIGHT(B$1,2),Sheet2!$D$1:$G$1,0))

Does that work for you?

Alternately, if you don't want to remove those spaces in Col A sheet1,

=INDEX(Sheet2!$D$2:$G$13,MATCH(TRIM($A2)&LEFT(B$1,4),Sheet2!$C$2:$C$13,0),MATCH(RIGHT(B$1,2),Sheet2!$D$1:$G$1,0))