Hi, trying to nail down issue?
I have a Giant Cypress Lx 8 speed.
The last two top gears won't let the chain advance but the others are fine.
Some suggested that the chain may be a couple mm too wide? tried adjusting front and rear no avail.
what is the standard size for an 8 speed hybrid bike? before I take it to a shop.
thanks.

Who suggested that the chain was too wide? Have you ever changed the chain? More likely that the RD just needs adjustment. Might need a new cable.

Top gears are the top ratio gears which will be the smaller rear gears on the bike? Or are they the low ratio gears which are the biggest rear cogs on the bike? Or are you describing the gears on the crankset?

If you messed with the two limit screws that are side by side, they don't do anything for your issue. They are only limits for how far the RD can move. If anything it's the barrel adjuster or inline adjuster you should probably have tweaked. But that isn't necessarily your issue. There are other things it could be.

Buy a 8-speed designated chain for a 8-speed cassette and there will be no problems. See if you can manually move the chain to these two cogs while rotating the wheel - if you have a bike repair stand, or get someone to hold the rear wheel off the ground so you can rotate the pedals. Sometimes it is a matter of checking for stiffness in the individual link attachment points which is going to be more of a problem with the smallest cogs where the radius is less for the chain.

This rings of limit screws or bent hanger. Limit screws are easy but useless if the hanger is bent. Your local bike shop has the hanger alignment tool. The repair should be covered under "shift adjust" for under $20-ish

Do the "top two gears" mean the largest cogs, which are the lowest gears, or the smallest cogs, which are the highest gear ratios? If the latter, it's probably excess friction in the cable housing, usually in the back loop at the derailleur. Remove the cable from the derailleur and see if it'll shift by itself. If so, work on the cable.

Usually, when a rear derailleur stops working, it's because something got bent. Usually the hanger. Check the hanger alignment before chasing rabbits down holes.

Thanks for all your replies, I'll look further into what has been suggested.
The bike has all new cables and shifters, issue is at the 7th & 8th gear on the rear cassette, and the largest chainring.
Works fine in all 8 gears when the chainring is in the smallest & middle but will only go up to 6 on the largest chainring.
& stiffens and won't go any further in the front chainring.

A 6-7-8 Speed chain is 7.2mm wide, or slightly less...
What you have described is a Chain LENGTH problem. Add four to six links to the chain and try it then.

That sounds as if the chain is too short

Check that the derailleur is able to swing backwards on its top pivot, and that it can spring back into place when released.