Your baby is almost four months old and holds a fairly sharper brain as compared to a new born one month old. Growth is permanent, which means that the brain also keeps developing with age. You as a parent need to help your baby's memory.
What you need to know
A 16 week baby would not be able to speak but he can express. You need to choose actions which can be repeated. For example- you can take a Walkman bring it close to the baby and play a happy song. Now when you would repeat the same action for the next two-three times, then the baby would get familiar with the use of the Walkman. In future, when you would hold the Walkman he would start to roll or chuckle because he would know music is about to be played.
Let the baby observe the different motions around him. Opening of the door, use of the light board, etc, are some regular actions which must be performed in front of the baby so that a good learning can be offered, which automatically gets saved in the memory of the infant. Some things aren’t taught but are analyzed by your baby himself.