difficulty in shifting to lower gear on shimano (6 speed rear gear)
There is a problem with the cable that links the shifter to the mechanism (rear derailleur)

The cable has become slack over time and needs to be tighter. You can tighten it by turning a barrel adjuster if there is one present. it might be as pictured and there might be one where the cable leaves the shifter on the handlebar. looking in the direction of the arrow, turn the barrel adjuster anti-clockwise to make the cable tighter.

Make small adjustments, ie one quarter turn at a time. You could search for videos to help. It's straightforward when you know how, but difficult and frustrating the first time. Your local bike shop would be happy to help you too.