Hello!
The latter is correct - it is the higher of the rolled d6 and the characters HP. If your character has 6 HP the "monster" must roll a 6 for a successful hit - subtract one from your characters HP.
In some cases a "monster" or character is given a bonus HP due to the specific type of encounter - these bonuses are described in the last section of some, but not all encounters. For example, rolling a 6 on the d6 GHOULISHNESS table gives the GHOUL +2 HP. If that same GHOUL has 6HP, instead of adding the two for 8HP, that GHOUL now rolls to attack twice (or gets two consecutive attack turns). Hopefully this makes the "monster" more powerful but still possible to "kill".
I hope this helps! Please let me know if you have questions!
Thanks,
Matt