I currently have a Shimano SLX derailluer (9 speed) with a Shimano 11-32T 9 speed cassette. Would there be any problem changing out the cassette for a Shimano HG400 12-36T 9 speed cassette? Thanks.

There's a possible problem with your rear derailer not being able to handle the largest cog. Changing the cassette would probably require you to adjust the B-screw. If you happen to know the exact model number of the rder, someone here might be able to help you; otherwise, you pretty much try it and see if it works.

I currently have a Shimano SLX derailluer (9 speed) with a Shimano 11-32T 9 speed cassette. Would there be any problem changing out the cassette for a Shimano HG400 12-36T 9 speed cassette? Thanks.

I'm seeing notes that the Shimano SLX M675 Shadow+ 10 Speed has the specs:

Rear Sprocket Sizes: 11T - 36T
Total Capacity: 35T

So, what chainrings do you have?

To be within Shimano's specs, you would have to have about a 10T difference between the largest chainring and smallest chainring.

Some notes are that specs can be slightly conservative. However, going over the max chain wrap, and it is a bit more tricky to adjust the chain length. It should be long enough to fit Big/Big rings, but can be loose or drag over itself a bit with the small/small combo. You have to decide if that is acceptable.

Oops, the M662 SLX shows:

Maximum sprocket: 34T

Chain Wrap: 35T (GS) or 45T (SGS)

So, it depends a bit on which derailleur you have. The SGS model has better chain wrap. The 34T is smaller than your target, but may be slightly conservative.

This should answer your question, assuming it is the same RD.

https://bike.shimano.com/media/techdo...9830616243.pdf

You may need a few more links of chain.