Figuring out the right Clockwork solutions is a mechanic introduced in Honkai Star Rail 2.0 that’s unique to the Dreamscape in Penacony.
It is first unlocked during the “Gentleness, the Name of Nocturne” quest when you’re tasked to follow Firefly to her secret location.
In your first encounter with cartoon Clockie, you’re asked to change the emotional state of a gang boss. The second Clockwork puzzle occurs when you come across a Bloodhound Family Member as you venture deeper into Dream’s Edge.

Warning: Spoilers if you haven’t completed “Gentleness, the Name of Nocturne”.
Clockwork solution to get past Bloodhound Family Member in Firefly’s quest

After meeting with Firefly on the roof, she tells you that her secret is hidden deeper in this part of the Dreamscape where The Family is still expanding and building.
Because it’s a restricted area, a Bloodhound Family Member stops you at the top of the staircase, for only authorized personnel are allowed past this point.
No matter what you say, he refuses to budge, which is when you’ll be prompted to use Clockwork.

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His current emotion is Calm, which means that you have the option to change it to Happy, Sad, or Angry.
Out of these three, two will fail, and only one is correct.
If you’re in the mood for some laughs, the dialogue that comes after Happy and Sad are pretty hilarious. Despite his drunk elation and learning how low he feels performing this job, the man sticks to his principles as hard as a nut.

The correct Clockwork solution is therefore, surprisingly, Angry.
Choosing this option instigates a battle with his odd-looking, hat-wearing orange guard dogs. It’s only after you win that he gives you the respect you deserve in dramatic fashion — and finally lets you through.
Sometimes, violence does solve everything.
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