There is a clog somewhere in the main line if your sinks backs up with water when the washing machine begins the drain cycle.
Washing machine and sink lines run congruent, and are often affected there is a clog backup.
Don’t turn to liquid drain cleaners or a plunger. Liquid drain cleaners are not recommended and plunging probably won’t work.
Calling a professional plumber will solve the problem simply and efficiently. A plumber will be able to determine where the clog location and will be able to remove it effectively.