The right that is not afforded by the Sixth Amendment is "The right to press charges in a countersuit against your accuser." The Sixth Amendment primarily guarantees rights related to criminal prosecutions, such as the right to a speedy and public trial, an impartial jury, being informed of charges, the right to confront witnesses, and the right to counsel.
The ability to file a countersuit is related more to civil law than to the rights protected under the Sixth Amendment.