atreya33 DirectX 9 is older than DX11 and as such, has fewer features, especially features that newer programs and newer hardware can use to run better. If you'd like to know more about what DirectX does, please see this:
https://en.wikipedia.org/wiki/DirectX
In general, there's a difference between "the sytem is compatible with and can run this software" and "the software is optimized for this OS or hardware." I don't know what's going on under the hood with Sims 4, but I would guess that DX11 mode has only been optimized for newer Nvidia and AMD GPUs to target higher-end gaming systems. I believe that any computer that can currently run Sims 4 also supports DX11, but that doesn't mean that this implementation of DX11 (as in what Sims 4 is doing) works with any system that supports the API in general.
I would guess that DX9 mode will be around for a while, at least until Maxis is satisfied with how DX11 mode works on any system it cares to support. (I don't know how long that would be, and whether it would end up like the Legacy Edition—opt-in for anyone as long as it exists—or only available to some users.) And I'm reasonably sure your computer can handle DX11 mode; the question is whether performance would be better or worse than in DX9 mode.
And yes, the fact that your system supports DX12 means it can also run DX11.