I understand you are having problems with the image when connecting an external monitor to the HDMI in your system.
It is important to mention that the computer you have has switchable graphics. This means that your computer has two graphics controllers, the Intel® HD Graphics 4000 and the Nvidia gtx660, and you have the possibility to select what to use or sometimes, the system automatically will change the graphics controller depending on the use.
Be aware that the special configuration in your system requires special drivers. We as Intel®, provide the hardware to the system manufacturer like Dell, HP, Toshiba, Acer, etc… and they will design and create customize drivers specifically for your system. Due to this, I suggest you contacting your computer manufacturer to get the drivers specifically for your system.