You can't. The mods that hexxit uses haven't been updated for Minecraft 1.6 yet. You don't need 1.6 much anyway - the mods work fine and you miss out on very little by just waiting until the modders have done their stuff and brought everything to the latest version of Minecraft.
If you have both the 1.5 and 1.6 minecraft launchers, is there a way to make sure that the Technic launcher will install the modpack to 1.5 and not 1.6? or does it do that automatically?
1.6 Minecraft manual install?
in Hexxit Discussion
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If you have both the 1.5 and 1.6 minecraft launchers, is there a way to make sure that the Technic launcher will install the modpack to 1.5 and not 1.6? or does it do that automatically?