STS-6
The STS-6 crew wore the standard AB Emblem embroidered mission emblems on their flight suits and on their in-flight clothing, thus there is no rare 'crew patch' for this mission.
Embroidered Mission Patches
A-B Emblem patch
The AB Emblem patch was the version used by the crew.
Lion Brothers patch
This version of the Lion Brothers STS-6 mission patch is the one most commonly seen. It has a plastic coating on the reverse.
Swissartex patch
The vintage version of the Swissartex STS-6 mission patch exists both with a waxy plastic backing and with a vacuum sealed clear plastic coating on the reverse. The fronts of the two versions are virtually identical.
Early Lion Brothers patch
This version of the STS-6 Lion Brothers patch is much more rare than the regular version. The fact that is usually has a bare cloth back implies this is likely the earliest version produced by the company but examples have also been seen with vacuum-sealed plastic backing, and even with a white plastic backing.
Cape Kennedy Medals blue border variant patch
This variant of the Cape Kennedy Medals patch has a dark blue border.
Cape Kennedy Medals white border variant patch
This variant of the Cape Kennedy Medals patch with a white border is less common than the blue border version.
Footnotes
[1] Example sales of STS-6 early Lion Brothers patches:
eBay item no. 331689199061 Oct 30, 2015, sold at $128.83
eBay item no. 262072965857 Oct 30, 2015, sold at $159 [plastic back]