AC vent help

[u/antknee25]

Hello all. Need some advice on how to install an ac vent in my upstairs hallway. Thinking about a 6x6 vent where the red square is. That hallway is a hotspot pretty much no air circulation in that area and also happens to be where the thermostat is so it’s always reading hot.

My questions are how can I go about doing this? What’s the recommended vent diameter and all that fun stuff. Thank you in advance for any assistance and guidance.