Nikon D3200 Raw file grain problem?

I edited raw photographs using Adobe Photoshop CS6, I saved them as JPEG. But when I uploaded it to photo sharing website and when I set it as my desktop wallpaper they're coming grainy. I've added a small patch of the photo for reference. Please tell me what should I do? I'm a newbie.

Thanks in advance!

There are many possibilities for this.

Using high ISO settings will produce more noise, but this looks like you have actually added some kind of film grain to the image in Photoshop CS6.

Have you adjusted the luminance settings? Usually starting at 25% is a good compromise, since while it will mask most moderate noise, it will still allow keep some detail in the image.

The same is true when adding sharpness in ACR. Keep it to a moderate level, like 25 of the possible 150

Check your settings. Do you have any add-on programs running with CS6?

How enlarged is that small patch, 100% or lower? After 100%, artifacts will start to show up.

Without seeing the whole image at full resolution, there's no way for most of us to pin point your issue and discuss any possible solution.

EDIT: Are you saying that you are a newbie using the camera. If so, stop doing much image modification using CS6. The best RAW processing program is really Adobe Lightroom 5, but you have CS6 so for now just make minor changes of your RAW image files

* very little sharpening, if any
* when shooting at high ISO's, make minor changes in Luminance
* enable lens profile correction
* in the camera calibration, use the Adobe 2012 using the Adobe Standard camera profile

Sorry but it's impossible to tell anything from that image you posted. It appears to be zoomed into to more than 100% - so all we can see is pixels.

First thing to do is open your RAW again in CS6. When ACR pops up, click on the main tab (Basic) and click the tiny menu icon to the right. Choose Reset Camera RAW Defaults. Make no changes whatsoever.

Set the zoom to 100% (no closer) and take a screen shot. Then upload the screen shot to tinypic.com and share the link here.

The 3200 is a cropped sensor, so it doesn terrible under a high ISO. A d610 or d800 is So much less grain