Mutiplying values based on criteria

so there are few ways and assuming you don't need any particular exceptions for having combinations that don't exist or have multiple options your could use FILTER.  I will use [ ] to indicate the related cells on that sheet and LU[ ] to indicate the LookUp table values so something like:

=[# cont] * FILTER( LU[multiplier], (LU[type]=[Cont type])*(LU[category]=[ODG]), 0)

but that said I like where Peter was going with using a formula to calculate the multiplier instead of a lookup.  Based on the pattern I see I might say:

=LET(
    TypeFactor, IFERROR( LEFT( [Cont type], 1) / 2 , 0),
    CatFactor, SWITCH( [ODG], "Y", 2 , "N", 1 , "OHOW", 4, "OHOW2", 6 , 0),
    [# cont] * TypeFactor * CatFactor
    )