The maximum number of electrons possible in the 6th energy level is 72. This follows the shell-capacity formula 2n², where n is the principal energy-level number: 2 × 6² = 72.
The sixth level is designated n = 6 and can contain six subshells: 6s, 6p, 6d, 6f, 6g and 6h. In the simplified shell-capacity model, these subshells together provide 36 orbitals, and each orbital can hold two electrons with opposite spins, giving a total capacity of 72.
A common mix-up is confusing the sixth energy level with the sixth period of the periodic table. The sixth period contains 32 elements because only certain subshells are filled in the ground-state configurations of known atoms. The level itself can hold more electrons than are occupied across that period.
The same formula applies to every principal energy level: the first can hold 2 electrons, the second 8, the third 18, the fourth 32, and the fifth 50.