As per https://www.nps.gov/zion/planyourvisit/the-zion-mount-carmel-tunnel.htm - "If your vehicle is 11'4" (3.4m) tall or taller or 7’10” (2.4 m) wide or wider, including mirrors, awnings, and jacks, you will need a tunnel permit."
Yes, I think I can. When I went to there, I drove a van.
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