[Indranil (OP)]

Why are the half-filled and fully filled orbitals more stable? Could you explain it, please? 

[chiralSPO]

It has to do with the "exchange energy," which is a measurement of the energetic benefit of having multiple electrons with the same energy and same spin.

It is a fairly complex topic, and is related to quantum mechanics that is probably far above what is require for the course you are taking, but you can read about it here: https://en.wikipedia.org/wiki/Exchange_interaction

The important thing to know is that the more electrons there are with the same energy and same spin in a small area, the more stable the arrangement is.

↑     ↑     ↑     ↑     ↑    

is more stable than

↑     ↑     ↑     ↓     ↓    

because in the top case, all of the electrons are equivalent and can exchange with each other, while in the bottom case, there is only a triple and a double.

The exchange energy is maximized when orbitals are half filled and completely filled.

[Indranil (OP)]

It has to do with the "exchange energy," which is a measurement of the energetic benefit of having multiple electrons with the same energy and same spin.

It is a fairly complex topic, and is related to quantum mechanics that is probably far above what is require for the course you are taking, but you can read about it here: https://en.wikipedia.org/wiki/Exchange_interaction

The important thing to know is that the more electrons there are with the same energy and same spin in a small area, the more stable the arrangement is.

↑     ↑     ↑     ↑     ↑    

is more stable than

↑     ↑     ↑     ↓     ↓    

because in the top case, all of the electrons are equivalent and can exchange with each other, while in the bottom case, there is only a triple and a double.

The exchange energy is maximized when orbitals are half filled and completely filled.

I understand the concept of half-filled orbitals. They are more stable because they have single electrons with one directional spin But what's about fully filled orbitals because each orbital has two electrons with opposite spins. In the case of full-filled orbitals, how the orbitals can be more stable? Could you explain it, please?

[chiralSPO]

The exchange benefit comes whether the orbital is filled or not.

If all p orbitals are half filled, then there are 3 equivalent electrons (one in each p orbital, and all with the same spin, let's say it's "up"). If all the p orbitals are filled then there are two sets of 3 equivalent electrons (the three "up" electrons can exchange, and the three "down" electrons can exchange.)

[Indranil (OP)]

The exchange benefit comes whether the orbital is filled or not.

If all p orbitals are half filled, then there are 3 equivalent electrons (one in each p orbital, and all with the same spin, let's say it's "up"). If all the p orbitals are filled then there are two sets of 3 equivalent electrons (the three "up" electrons can exchange, and the three "down" electrons can exchange.)

What do you mean by  'there are two sets of 3 equivalent electrons? As I know there are three sets of electrons in p orbitals. Could you let me clarify it, please?