For the sample shown try:
=B4*SUMPRODUCT((Sheet2!F$4:F$8=A4)*(Sheet2!H$3:J$3=C$2),Sheet2!H$4:J$8)
Assuming that the actual data may be extended through December modify the formula to read:
=B4*SUMPRODUCT((Sheet2!F$4:F$8=A4)*(Sheet2!H$3:S$3=C$2),Sheet2!H$4:S$8)