You should enter the amounts in each Box 16 as they appear on your W-2s. As a Massachusetts (MA) resident, all of your income is taxed by MA regardless of where you earned it. New York (NY) considers someone working remotely (telecommuting) for a NY company as working in NY, and therefore taxes them as a NY nonresident. The amounts in Box 16 for each state only indicates the amount of the income in Box 1 that is taxable by that state. It will not double your taxable income, rather it means that 100% of the amount in Box 1 is taxable by each state. As a Massachusetts resident, Ma will give you a credit on your MA tax return for the income tax you pay to another state, in your case the tax you pay on your New York non-resident tax return. The amount of the credit may be less than the actual amount of tax you pay to New York.
There are situations where remote income is not considered taxable by New York. To determine if your remote income will be taxed by the State of New York see the following TurboTax article: Is my remote income taxable in New York State? [Edited 01/26/25|1:40 pm PST]
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