2 cores doesn't really indicate anything meaningful without more context. Cores from different generations aren't equivalent, and even cores across models within a generation vary significantly in terms of performance. With that said, 2 cores is possibly ok for simple web browsing or other general (non-computationally intensive tasks). But real-time video encoding requires either a dedicated encoding offload chip (as many mobile devices have, as well as dedicated GPUs like nVidia with their NVENC [AMD has one but piss-poor software support, so I'm ignoring then in OBS context].
in your case, if you mean the 6 generation old i6-6xxxU CPU.. see comments above. qhobbes already told you some settings. and see my post back in Oct. You will need to optimize the OS to turn off eye-candy and unnecessary processes, and minimize resource demands in OBS. and then, .. maybe..