If the P-trap is empty but both sinks remain deeply flooded, the clog is deep inside the horizontal drain pipe behind the drywall. You will need a manual plumbing auger (drain snake). Remove the P-trap using the steps outlined in Method 5.
When you feel the cable hit resistance, you have reached either a sharp pipe bend or the clog itself. Tighten the thumbscrew on the snake drum. double sink clog