Can I upgrade my iPad 2 Operating system to iOS 6?

Yes.

Upgrading iOS

1. How to update your iPhone, iPad, or iPod Touch

2. iPhone Support

3. iPod Touch Support

4. iPad Support

a. Updating Your iOS to Version 6.0.x from iOS 5

Tap Settings > General > Software Update

If an update is available there will be an active Update button. If you are current,

then you will see a gray screen with a message saying your are up to date.

b. If you are still using iOS 4 — Updating your device to iOS 5 or later.

c. Resolving update problems

1. iOS - Unable to update or restore

2. iOS- Resolving update and restore alert messages