"In the figure below" or "in the below figure"?

Solution 1:

The first example is correct, not the second.

Below is generally used as an adverb or preposition, not as an adjective. See, e.g., Cambridge.

As such, it does not modify figure.

In the first example, it could be construed as either, based on what is implied.

As a preposition

In the figure below [this spot] . . .

Or as an adverb

In the figure [shown] below . . .

Solution 2:

They're both correct, and amount to the same thing, but the second use of below as an adjective is less common.

So uncommon in fact, that you can find native speakers complaining to lexicographers about it. That in itself may be a reason to avoid it, though it has nearly a century of attested use.