Problem:

Matrix1 (cells A3:D6) and Matrix2 (cells F3:I6) have a similar structure.
Range A8:C11 contains pairs of index values, representing columns and rows for both matrixes.
We want to create a formula to multiply the corresponding values from each matrix that are stored in the positions indicated by each pair of index values.

Solution:

Use the INDEX, OFFSET, and MATCH functions in the following formula:
=INDEX(OFFSET($A$3:$D$6,1,1,3,3)*OFFSET($F$3:$I$6,1,1,3,3), MATCH(B9,$F$3:$F$6,0)-1,MATCH(A9,$A$3:$D$3,0)-1)