Duel Monitors e6420

@Falcon1776  looking at photos of the Latitude E6420, it appears the only standard video output connector built into the system itself is a VGA output, which you can't use to drive multiple independent displays.  If you don't want to get a dock, your only other option would be to use an adapter that relied on "indirect display" technology such as DisplayLink -- not to be confused with DisplayPort.  Those adapters plug into a USB port and then give you an HDMI, DisplayPort, or VGA output.  Plugable makes such adapters and they have a reputation for quality products.  However, DisplayLink technology requires that DisplayLink software be installed on your system, so if you don't have admin access to your system and your IT department wouldn't be willing to add it, then you wouldn't be able to use those adapters.  The only other way to get multiple independent displays would be to get an E-Port or E-Port Plus dock.  The former would allow you to use dual displays as long as one of them was connected via VGA (the other can use either DVI or DisplayPort, and you can use DisplayPort to DVI/VGA/HDMI adapters there as needed), whereas the E-Port plus includes two DVI outputs and two DisplayPort outputs, so you can use two displays via any combination of those outputs if desired, without having to resort to ancient VGA for one of them.  Or you can do that with the Plus dock if you want to.

@Falcon1776  one more note in addition to my reply above.  With an E-Port dock (both regular and Plus models) you need to use a 130W power supply.  Docks sold by Dell always come with those, but some third-party vendors will sell you only the dock unit without a power supply.  If you go that route and don't have a 130W power supply to plug into the dock, then the dock might not work properly.  You should NOT expect to be able to use your system's own power supply through the dock, because system power supplies are typically 65W or 90W, and that typically isn't enough power when running through the dock because the dock needs to reserve some power for itself to run its internal electronics and power any USB devices you might plug into it.  That's why the power supplies that come with docks have higher wattage output than the ones that are designed to be plugged directly into the system that you would be docking.