If you are trying to unclog a double sink drain, you'll need to target the one drain that both sinks flow into. Each sink has it's own drain and a shared draining pipe system. If clogged, the drain prevents water from leaving one or both sinks.
Plug one sink then use a plunger on the other which should cause enough pressure into the one drain to and unclog the sink. If that does not work, mix 1/3 of a cup of baking soda in with 1/3 cup of vinegar and let it sit in the drain for an hour then flush it with boiling hot water.