Alternately if this is something you need to do often build an inverted hash with the keys and values switched.

my %hash_inverted;
@hash_inverted{ values %hash } = keys %hash;
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Just remember that this won't be automagically updated so if you update %hash you'll need to also update %hash_inverted (and/or wrap them both up in an object and let that keep things updated for you when you use its accessors).

Update: Good point below about duplicates, which also brings up the point that if your original hash has non-scalar values you may need something like Tie::RefHash for the inverted version.