Inherited this bike and it's got this strange gear shifter that I don't understand. The one on the right is one to five with six spaced a little further away. It's got a 3 and 6 cog derailleur as you'd expect but I can't work out how this works. It's also all really stiff and hard to move which makes it a pain to test out.
Looks like the left-hand front shifter has multiple positions to allow you to adjust the front derailleur to avoid chain rub when shifting through the rear sprockets.
The shifter is probably corroded inside which is making the action very stiff - notice the rust on the central screw. The cable and front derailleur may also be contributing to the stiffness.
If you can get some light oil inside then work the shift action repeatedly you may get it to free up some. You can disassemble it, clean the internal components, lube with grease and re-assemble. If you are unsure about getting it back together properly, taking frequent pictures or even making a video of the disassembly process can help you remember where all the components are supposed to go.