Read this before the following hints!

Hint 1 of 7:

The key to solving the rest of the puzzles on this screen is having someone
to help you.

Hint 2 of 7:

You'll need to help hatch something to get that help (no, not the
boucassier).

Hint 3 of 7:

Look in the store for a boa-boa egg.  If you can get the egg to hatch, you'll
have the help that you need.  (See the hints about the store if you don't yet
have an egg.)

Hint 4 of 7:

Again, you need to incubate the egg.

Hint 5 of 7:

The same way that you incubated the boucassier.

Hint 6 of 7:

You'll have to go into the alchemist's lab before you can solve this puzzle
-- for some reason, it's the only place that you can use one inventory item
on another.

Hint 7 of 7:

Use the boa-boa egg on the hot water bottle (via the right hand), and the egg
will hatch.  Fulbert will join you when you go back into the main part of
town.