I have installed Deore derailleur GS on a 10s cassette where the largest cog is 42T. When I shift to the 9th cog, it rubs with the derailleur. It seems the cage is not going under the cog. Do I need an extension? See attachment pic.0

According to Shimano specs that derailleur is 42T compatible.
https://bike.shimano.com/en-EU/produ...-M6000-GS.html

Edit: upon closer inspection it looks that what you have is in fact the SGS version which is rated only for 36T. Then yes, you need a derailleur extension for it to work with 42t casette.
https://bike.shimano.com/en-EU/produ...M6000-SGS.html

Hi, no it is GS. According to where I bought it.

Is the chain length correct? If it is, adjust the end adjust bolt to make the guide pulley to drop lower, per the manual.

Compare it to the pictures in Shimano's site, both versions look slightly different (the paralelogram and the clutch area). Looks like you've been given the wrong one. The model name should be somewhere on the back of the paralellogram, check for it.

I will check the name tomorrow. So, what's the quick solution now? Extension? I do not want to play with B screw.

Seems to me the quick solution is to check that you bought the right thing and take it back if you didn't.

The B screw is a normal adjustment. It should always be "played" with. Why is your Q/R skewer on backwards?

That was my first thought.

I know, I put the wheel faster earlier. Tomorrow will reverse it. I ordered an extension by the way.

Sometimes it is just a matter of getting the setting on the "b" screw correct. I didn't like the way the SRAM X7 RD performed on my recumbent trike with an 11-36 cassette so I switched to Shimano. I used the guidance offered by the Sheldon Brown website to buy the right Shimano derailleur. They warned it would not work right with the b screw sent by Shimano but switching to a longer b screw would allow the RD to clear the 36. They were right. It's been in use now for 6+ years and shifts perfectly. Before you take it back, try adjusting the b screw.

It works i adjusted the B screw. I bought the extension in vain. I will sell it on ebay.

Extensions can cause poor shifting, as it reduces the angle/force of the chain against the next cog, due to the jockey being further away.

It's important you use a cassette within the rated range of the derailleur, and adjust the B-screw accordingly, so the jockey is the correct distance from the cassette rings.

Your derailleur has a switchable clutch, you need this in the 'on' position when in use, only off when working on the bike.