This expression means “would prefer to”, and is followed by the infinitivewithout to. We often use the contraction’d rather.
Would you rather stay here or go home ?” I would rather stay home in weekends than go to the beach.
When we say that we prefer one activity to another, two –ing forms can be used. The second can be introduced by to or rather than (more formal).
I prefer staying in hotel to staying in appartment. Prefer can also be followed by noun. I prefer coffee to tea at the afternoon.