I have a MacBook Pro A1278 Model, One RAM slot is not working. I am currently using 2gb ram in Single slot that makes my laptop slow. My question is can i put 4 or 8 gb ram in working slot so that my Mac can run smoothly??

A1278 looks up to 13-in MacBook Pro models released from 2008 through 2012.

the oldest (and therefore likely most restrictive) is described this way:

Standard RAM:

2 GB

Maximum RAM:

8 GB*

Details:

2 GB of RAM is installed as two 1 GB modules, no slots free. *Apple officially supports a maximum of 4 GB of RAM. Originally, this model was only unofficially capable of stably supporting 6 GB of RAM, but as confirmed by site sponsor OWC, it is capable of supporting 8 GB of RAM if updated to Boot ROM Version MB51.007D.B03 and running MacOS X 10.6 "Snow Leopard" or higher.

from:

https://everymac.com/systems/apple/macbook/specs/macbook-core-2-duo-2.0-aluminum -13-late-2008-unibody-specs.html

So it seems very likely that (provided your firmware is up-to-date) you could install a 4GB DIMM with the exact correct specs in that model, and have it function as the only DIMM, and provide 4GB of RAM available.

Any conflicts that restricts you to 6GB total are conflicts with other devices in the total Address space, not conflicts with DIMM addressing in a slot.