Answer
Ionization energy increases as the ionization number increases because removing electrons reduces the repulsive interactions, making removal of the next electron more difficult than the last.
Work Step by Step
Carbon has 6 electrons. For $I_1$ to $I_4$ the valence electron is in the second shell. As each electron in turn is removed the repulsive interaction between the electrons decreases, requiring more energy to remove the next electron.
There is significant jump in the ionization energy for $I_5$ because the final two electrons are in the first shell. These two electrons are closer to the nucleus and are not shielded, so are subjected to more force from the nuclear charge. This force makes these two electrons more difficult to remove.
$I_6$ has the greatest ionization energy because all the repulsive energy has been removed with the removal of all but the final electron.
