Approx. 3 weeks ago I found an abandoned frame (including handlebars, fork, brakes, pedals and shifting gears attached to it). I decided to use it to build a new bicycle since only recently I've decided to learn more about these things (even though I have been riding a bicycle since the age of 3 :D). A friend of mine gave me an old MTB 2 months ago for spare parts if I need any. I decided to use the wheels (including the freewheel hub on the rear wheel) since they seem to be in order especially after cleaning and oiling the bearings and axle, and diameter-wise they are a perfect fit - 26 inch (actually my initial intent on mounting the wheels on the frame was to see what wheels would fit on it).
The problem I'm facing is that according to a friend of mine the shifting mechanism is meant for at least 8-speed rear freewheel hub while the freewheel hub the wheel from the old MTB has only 6 cogs.
My first question is what the model of the shifting gears is? The only thing that I have found are the labels on the various components that are part of the whole gear thing and they seem to be all part of a Shimano Deore XT set. Sadly when I looked online I found out that there are like 10 or so versions of this set throughout the years since the initial release. The parts look relatively new so I would exclude all models that are older than let's say 2005-2006 (correct me if I'm wrong). Is it really meant for 8/9-speed?
My second question is if it's possible to change the freewheel hub with a 8/9-speed without a need for replacing the whole wheel itself? The question of course applies only if the answer to the first one is "Yes, this is not a 6- but a 8/9-speed freewheel hub". This is probably a dumb question but since I've just started learning I don't want to screw things up. IMHO it shouldn't be a problem for close values (like 6 vs 7 speed if such a thing exists) since (to my understanding) rear cogsets with lower number of cogs have a greater distance between adjacent cogs while cogsets with a higher number of cogs have a smaller distance between adjacent cogs which makes me believe that in terms of width cogsets are in general similar enough and I shouldn't be bothered when switching on freewheel hub with another. I have another freewheel hub with 7 cogs from my previous bicycle and based on the measurements I've made the width compared to a 6-speed cogset is very small.
Below are some photos of the gears I have. Cleaning is currently undergoing so don't mind the rust and dirt. :D
If you need more information/photos I can provide these.
UPDATE: After doing some testing and also after looking closely at the rear derailleur I found that it's a Shimano Deore XT RD-M760 which - according to multiple sites - supports 7,8 and up to 9 speeds. I actually have a 7-speed freewheel hub from my previous bicycle however I am considering buying a 8-speed one. The chain I bought is a KMC Z8S which has 116 links in total (I have cut it to fit my wrong 6-speed configuration but I have a spare master link plus the rest of the chain so I should be able to recover from this mess :D). The labelling on the casing says that it's meant for 18, 21 and 24 speed systems hence with the 3 speeds on the front I can use this chain with a 6, 7 and 8 speeds on the rear. However due to my gear I have to stick to either 7 (that is 3x7=21) or 8 (that is 3x8=24) speed freewheel hubs. Given that I have an indexed shifter (as pointed in the comments) and some research I did I should go for an 8-speed freewheel hub, right?