Making a HDMI switch basic question
Use this Analog Devices part. It is "AD8191:  4:1 DVI/HDMI SWITCH WITH EQUALIZATION". Unfortunately they don't make more than a 4:1, so you will have to cascade them. More choices here.

However, I fear if you couldn't find these parts, you might be in over your head. As kenny pointed out, this isn't easy due to the data rates and edge speeds. Signal integrity and controlled-impedance PCB issues aren't something I would wish to deal with on a hobby project.