On my bike I have 7 gears at the back and 1,2,3,4,5 are normal and shift fine but some reason I can’t shift to 6 the lever or switch won’t go and feels stiff I’m unsure what it is I thought it might be a tight cable somewhere or the actual shifter.
Check the limit screws on the rear derailleur. Without knowing exactly what kind of derailleur you have, it's difficult to be more specific, but these are probably two small screws coming out the back; one limits the derailleur's inside travel, the other its outside. It may be that one is tightened too much.
There's also (usually) a barrel adjuster, either where the cable enters the derailleur, or where it exits the shift lever; if this is backed out too far, it will tighten the cable, preventing you from shifting all the way through the gears, although it's hard to imagine it could block out two gears.
Sounds like you are having trouble shifting to the two largest sprockets (lowest gear ratios) because the downshift lever needs to pull cable and can be jammed, whereas the upshift lever releases it.
The jam could be in the shift lever, the cable run to the derailleur, or the derailleur itself. Here's a procedure to track it down:
- Disconnect the shift cable from the derailleur
- With the back wheel off the ground, turn the cranks by hand and manually push the derailleur inwards by hand (being careful not to catch your fingers in the chain). If the derailleur wont shift to the largest sprockets, the problem is there. Check for any debris in the parallelogram. The issue could also be with the limit adjustments.
- Put some tension on the shift cable and try to click up and down through the gear positions. If the shifter will not go to the lowest gears the cable may be jamming or shifter could have debris in it.
- Pull the housing back off the cable where it enters the shifter and introduce a little slack, try to click up and down through the gear positions again. If the shifter still wont go to the lowest gear positions the problem is in the shifter.
If the problem is in the cable you can try tracking where the jam is be inspecting the cable run. Sometimes you just need to replace the cable and housing - they are technically wear itms and not very expensive.
A jammed shifter if a bit trickier to deal with. There are some existing questions and answers on this site that deal with that.
Finally, you should go through a systematic rear derailleur setup procedure. This will sort the limit adjustments out if that was the problem.