I tend to recommend the following process:
Install the pack via Twitch
Install the version of Forge that the pack requires
Make a new "Installation" in your launcher, setting its "Minecraft Version" to the correct version of Forge for the pack and setting its "Game Directory" to the folder that Twitch installed the modpack to
Run the pack with the normal Minecraft Launcher
This usually fixes things as the most common issue with Twitch is they managed to screw up Forge's install process