I have many pictures that I have taken on the RAW setting for editing purposes on my Nikon D3200 camera. I am able to zoom in on a subject in the picture but cannot figure out how to save that zoomed in picture. For instance, in quick edit mode I can zoom in on a bird in the picture bringing it into closer view but cannot save that zoomed in picture- Is there a way to do this?
I'm going to guess you're not doing this in-camera, but in Photoshop Elements. If so, in Quick Edit mode, don't zoom in, just select the Crop Tool from the tools menu (shortcut is the "C" key on your keyboard). You'll get a frame you can position around the area you want to save.
Assuming you are using the D3200 in-camera editing features:
The Quick Retouch option will only allow you to edit and save the amount of auto saturation and contrast. It allows you to zoom to get a better view of a particular part of the picture, but you cannot save a crop from that option.
You need to use the Trim option that is near the top of the list just below D-Lighting and Red-Eye Correction.
It is all on page 152 of your Reference Manual.
With NEF (RAW) files, I would recommend you first use the NEF (RAW) processing option outlined on page 157 and then apply the crop to the new JPEG saved from that operation using the Trim menu option.