There is a rule the is usually followed when making the most stable electronic congifuration of elements.
It is as follows:
Where we from up to down following the arrows. s means it can hold up to 2 electrons, p can hold up to 6 and d can hold up to 10.
Palladium has atomic number 46, so, in its neutral form, it has 46 electrons.
We start by putting 2 into 1s, to get 1s².
The next 2 goes to 2s, to make 1s²2s².
Then, we go to 2p, so we can put 6 now to get 1s²2s²2p⁶.
For now, we have used 10 of the 46 electrons, so we need to continue.
Next we have 3s then 3p, so we get 1s²2s²2p⁶3s²3p⁶.
Then, we have 4s, so we have 1s²2s²2p⁶3s²3p⁶4s².
Now, we need to go to 3d, which hold up to 10 electrons. We used so far 20 electrons, so we can continue. We put 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰.
Next we 4p and 5s, so we get 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s².
We have used 38 of the electrons so we only have 8 left. The next is 4d, but since we only have 8 electrons left, we can fill only up to 8, to get 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d⁸.
So, the final electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d⁸