What is the electron configuration of #"Ti"^(2+)#?

A good place to start when trying to figure out the electron configuration of an ion is the electron configuration of the neutral parent atom.

In this case, titanium, #"Ti"#, is located in period 4, group 4 of the periodic table and has an atomic number of #22#.

This means that a neutral titanium atom will contain #22# protons in its nucleus and #22# electrons surrounding its nucleus.

Therefore, the electron configuration of a neutral titanium atom must account for #22# electrons. Consequently, the electron configuration of the titanium(II) cation, #"Ti"^(2+)#, must account for #20# electrons, since this cation is formed when a neutral titanium atom loses #2# electrons.

The electron configuration of a neutral titanium atom looks like this

#"Ti: " 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2#

Now, it's important to keep in mind that this notation for the electron configuration is useful when adding electrons to build an atom "from scratch" because in that case, the #4s# orbital is filled before the #3d# orbitals.

That happens because the empty #3d# orbitals are actually higher in energy than the empty #4s# orbital, as seen here

However, once the #4s# orbital is filled, it becomes higher in energy than the #3d# orbitals. This means that when titanium loses electrons, it does so from the #4s# orbital first.

#"Ti: " 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2 4s^2#

Therefore, the two electrons that are lost when the #"Ti"^(2+)# is formed will come from the #4s# orbital, which means that the electron configuration of the cation is

#color(green)(|bar(ul(color(white)(a/a)color(black)("Ti"^(2+): 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2)color(white)(a/a)|)))#

If you want, you can use the noble gas shorthand notation to write

#color(green)(|bar(ul(color(white)(a/a)color(black)("Ti"^(2+): ["Ar"] 3d^2)color(white)(a/a)|)))#

Here #["Ar"]# represents the electron configuration of argon, the noble gas that comes immediately before titanium in the periodic table.