lookup multiple cells with corresponding multiple criteria based on one table

Hello,
I've been trying to find an answer to this question online - so far no success.
I have a table of several types, where each type has two values (Z1,Z2)
I have another table, with 6 rows, in each row several instances of the types from the first table, with no specific order.
I'm trying to calculate the TOTAL Z1 and Z2 values of all the instances in each row.

Any idea?

Thank you alllookup table.jpg