Buoyancy is the net force of all the particles hitting the surface of the block. Regardless of the liquid type, there are forces pushing up, down, left, right, etc.
In general, the pressure is dependent on depth. So the highest pressure is in the lowest part. If the wood is completely submerged in a single liquid, that means the liquid on the bottom is pushing up harder than the liquid on top is pushing down. The net result is upwards buoyancy.
In this case, there isn't any of the blue liquid above the block, so the only force is pushing up. Obviously, this is a net force pushing up.
Likewise, there's none of the green liquid below the block, so the only force is pushing down. Again, there's an obvious net force, this time down.
The net buoyancy will be the combination of the two. The green liquid is necessarily less dense (or it would fall below the blue liquid), plus it's higher, so its total pressure will be lower. Ergo, the net buoyancy will be upward.
This is the same as what happens when the block is floating on top of the water. The air above the water is your second fluid in that case.
If the net buoyancy is pushing up harder than gravity pulls down, the block will move upward. If buoyancy is lower, the block will move downward. When the buoyancy exactly equals gravity, the block will sit in one spot.
Generally, if the block is more dense than both liquids, it will fall to the bottom. If it's less dense than either liquid, it will float to the top. If it's between the two densities, it will float between them like the diagram shows.