The best thing you can do when trying to improve hand-eye coordination with your child is to let your child play with the toys on her own.
You may feel the urge to show your child how it works. But part of the fun with hand-eye toys is figuring out how they fit together and work.
To improve hand eye coordination get some blocks or tower toys. Let your child build things with blocks that encourage playing and coordination. These toys help your child learn what items can fit on top of each other and stack easily.
By the time your child reaches two or three years of age, she’ll be ready to start throwing things and wanting to catch them. This is a great way to improve hand-eye coordination.
Infants and toddlers build concepts based on their sense and motor explorations. For example, they learn the difference between wet and dry, soft and hard, rough and smooth, cold and hot, movable and stationary. From: Early Childhood Resource Institute
Toys that involve fitting things together (like stackable bowls) help hand-eye coordination. From: essortment.com