You can easily jailbreak iOS 6 Beta 4 on your iPhone or iPod touch using RedSn0w 0.9.13dev3. It is as fast as counting 1, 2 and 3. Simply follow the below guide to jailbreak iOS 6 Beta 4 on your iPhone or iPod touch via RedSn0w:
How to Jailbreak iOS 6 Beta 4 on iPhone and iPod touch
Step#1: Download and install the Redsn0w 0.9.13dev3. Extract the zip file and store its content in the hard drive or any other location which is easy to remember.
Step#2: Now download the iOS 6 beta 3 IPSW firmware (only available for developers). Restore the downloaded iOS 6 beta 3 IPSW firmware file on your iDevice via either Xcode or iTunes.
Step#3 (Precautionary step): It is recommended to create a complete backup of your device when jailbreaking it. In order to create a complete backup of your iDevice, connect it to the iTunes using a USB cable. You can also backup your content on iCloud.
Step#4: Now launch the Redsn0w and choose “Extras” from the menu ahead of clicking the “Select IPSW” option.
Step#5: At this point click on the “Select IPSW” option and browse the iOS 6 beta 3 firmware file that you had downloaded earlier.
Step#6: Now select the “Jailbreak” option from the main menu.
Step#7: Now follow the on-screen guide from RedSn0w in order to put your iDevice into the DFU mode (screenshot below):
Step#8: Now leave the rest on RedSn0w. As this is a tethered jailbreak you will need to boot into jailbroken state whenever you restart your iDevice. You can simply do so by connecting your iDevice to the PC or Mac via a USB cable and launch RedSn0w. Select “Extras” option and tap on “Just Boot” and follow the instructions that appear on the screen.