First, we take the feeders and fit them into the boxes. To determine which answer goes in which box, we look at the 15-puzzle at the bottom and notice that some tiles are lava tiles and some are not. The lava tiles only contain the letters LAVA. The flavor text says that lava obstructs, so we need to cover half of each feeder with LAVA. The other half must contain only letters that show up in non-lava tiles. Using this, we get a unique solution:
M
L
L
A
V
A
L
A
R
A
I
N
I
V
O
A
L
I
A
A
M
O
R
P
V
E
L
A
V
A
A
T


Now we make these formations in the 15-puzzle. We see in the flavor text that lava illuminates, so we look at the red letters (not the letters inside the coins) illuminated by the lava to see what word they form. Each word corresponds to one of the input puzzles:

Puzzle Word
The Lava Line BATS
Fighting with Fire FUEL
Red-Hot Cog Rolling PROM
Magma Group WIND

We look at the middle diagram with the 4 red coins to see where to place each of these words. When we do, we recreate the pattern in the 15-puzzle, giving TERMINAL LAVA SOUP.