Adding gears to my grandson's 12" bike My grandson has the kind of bike you pedal backwards to brake, and he goes riding with me on my days off.  Yesterday, he asked me if we can convert his bike because we have looked everywhere and no one seems to have a gear-shifting bike for someone who is 8.  The Problem is that he is having trouble keeping up with me and wearing out a lot earlier because of the hills.  Are there bikes with 18" or less wheels that shift or is he still too small for that kind of riding?  I am pretty sure that I can figure out how to mount the gears and get a small derailleur just to learn how to shift and I am pretty sure I can change his brake system to the handlebar levers, but not sure it would be so wise, if I could just get his parents, who are willing and more financially able, to replace the bike with one that is built to be a dirt bike and not a trick bike frame with attachments to help him go faster.

I am pretty sure it is possible and I may even be able to make it just like mine but not sure how cost effective it is if he can just buy one.

I am still learning what different bikes are called.  But he is about 3ft tall and his bike is getting too small for him.  His current bike has 12" wheels.
If your grandson is that young, he's likely to have trouble keeping up with you no matter what bike he's riding. It may be that it's your expectations, not his bike, that should be modified.

It seems really unlikely that you could retrofit a derailleur onto his current bike. A frame that small won't have room for a wider rear-wheel assembly. Mounting rim brakes would be tough if the frame isn't already set up for it. Even if you did succeed, he'd still be driving it with eight-year-old legs and an eight-year-old's heart and lungs.

Might you consider a tagalong bike, mounted to your bike? Your grandson might balk at this if he's used to his own separate bike, but it would ensure that he keeps up with you.