While I couldn't find an official statement that the laptop can handle three displays, if you look up your video card it does show up on Intel's list of supported three-display configurations. I'm going to go out on a limb and say you don't also have an AMD GPU in your laptop - if that's showing up in your Device Manager you may have a bad driver or something else going on, which brings us to the first order of business:
1. Update all of your drivers.
Intel probably has some sort of built-in software you can use to manage your display settings - you don't necessarily need to update that, but definitely make sure everything under "Display adapters" in Device Manager is up-to-date - you can uninstall it/them and restart your machine if needed, as the driver(s) should auto-reload and you can check for fresh updates.
2. Test the two external monitors without the laptop display
Make sure you edit your power settings to not make your laptop sleep when you close it, connect both monitors, and then close your laptop lid. As long as one monitor displays you can troubleshoot the other from there - it's important to make sure they can both be detected at the same time and that they are each set to a compatible resolution (if one has a VGA and one has an HDMI, I would imagine the resolutions will vary).
3. Bring the laptop display back into the mix
If you can get both external displays working, open your lid back up - it may be good-to-go right off of the bat, or you may have to tweak some other resolution/display settings; sometimes a computer can support three-displays but not necessarily be able to extend to three (i.e. two displays may have to be duplicated).
Ultimately: even after you make sure everything is updated, sometimes getting your displays to all come up correctly just takes some playing around with. It's a familiar dance of power-cycling, unplugging cables, plugging them back in, and changing your settings. Let us know if this helps at all and we can go from there.