Hello Nagaraju, this is a great question and I am glad you asked it. The reason for this is that there are energetic considerations that have to be accounted for. It is more favorable for an atom to fill its 4s shell before its 3d shell. This is is due to a couple of different factors that I won’t go into here but come from a the electron orbitals’ closeness to the nucleus and orbital momentum too. Attached is an image of how to consider the filling of the orbitals. Write out the lines pictured and draw arrows going down and to the left to pass through all of the orbitals. This will give you the order in which the orbitals are filled.

Why do we have 2 arms and 2 legs? It's the way we are.

Similarly, atoms have electrons that are arranged in specific ways, starting with the innermost 'K' or '1' shell that has 2 's' electrons when the shell is full. Hydrogen only has 1 's' electron. That electron easily leaves the H atom to give the hydrogen ion, or proton, H+. The electron attaches to an atom that has space for an extra electron in its outermost shell. The diagram for the distribution of the 's' electrons is a sphere centered around the nucleus.

The next shell - 'L' or '2' - has 2 's' electrons and 6 'p' electrons when it's full. The diagram for the distribution of the 'p' electrons is like 3 dumbbells pointing in the X, Y, and Z axes, centered at the nucleus.

The next shell - 'M' or '3' has 2 's' electrons, 6 'p' electrons, and 10 'd' electrons.

This wikipedia article says the electron shells were discovered with X-ray absorption studies: wikipedia electron shells.

I like this section, with the numbers of electrons in each shell for each element: here.

My brother can't understand how snowflakes can form with 6 identical points. The snowflake expert talks about how this happens, but it doesn't make sense to my brother.

In order to fully explain this, I would need to understand quantum electrodynamics and you would need to understand enough math in order to comprehend quantum electrodynamic (it involves a lot of calculus). In short, the answer is 'no', it's not easy to explain.

What I can explain is the mathematical pattern of the number of electrons in each shell. The number of electrons in each shell is given by the following equation:
N = 2 x (l ² ), where N is the number of electrons per shell, and l is the level of the shell. So, the first shell has two electrons, the second has eight, the third has eighteen, the fourth has thirty-two, the fifth has fifty, the sixth has seventy-two, and so on.

The general reasons for this include the following:
1. No two electrons in the universe can have the same quantum numbers. Quantum numbers include physical location, but also energy level, as well as a property called 'spin'.
2. The reason why every electron shell has an even number of electrons is due to spin An electron can either have spin of +1/2, or of spin -1/2; thus, two options. Electrons are leptons, not bosons, which is why their spin is not an integer and cannot be zero.
3. The electron shells themselves are energy levels, but they have different slots. This follows a law of squaring each number for the size, i.e. 1, 4, 9, 16, 25, 36, and so on.
4. Electrons will drop energy into the lowest energy level possible, emitting light as they do so. All atoms have higher electron shells, and indeed have an infinite number of higher shells, but usually only the shells near the bottom are occupied by electrons, due to electrons' radiating away their energy as light as they fall to lower shells.

I do not understand why no two leptons in the universe must share the same quantum numbers. I do know that bosons (such as photons) are not subject to this limitation.

I do not know why bosons have integral spin and leptons half-integral spin, or even really what spin is. This is a property of quantum physics that I don't understand, but I do know exists.

I do not know why the energy levels have slots as the squares of the integer of the level. I do know why it's 1, 4, 9, etc., though; that's just math.

I do know that the reason why electrons jump to lower energy states is because of the second law of thermodynamics: having light zipping off to infinity is a higher-entropy state than having the energy stored in the electron at a higher energy level, so electrons will preferentially radiate away their energy.

For filling the 4s orbital before the 3d orbital, the rule we follow here is one that considers the energy levels of the orbitals. The 3d orbital, though smaller in the number of n, has a higher energy than the 4s orbital, at least according to the atomic model we currently adopt. The reason for the higher energy of the 3d orbital has to do with the angular momentum of the electrons in the orbital. In simpler versions of atomic models, we learn that these orbitals with higher angular momentum will be filled later, but this version of the model is not the complete picture, and the complete picture requires an understanding of the quantum mechanical model, so you may have to read more about quantum mechanics to learn the deeper reasons.