To determine how many electrons a magnesium atom must lose to achieve a filled outer shell, we start by examining its atomic structure. Magnesium has an atomic number of 12, which indicates it has 12 electrons. The electron configuration of magnesium is represented as 1s² 2s² 2p⁶ 3s². This configuration shows that magnesium has two electrons in its outermost shell (the 3s subshell).

In order to attain a stable electron configuration similar to that of the nearest noble gas, neon, which has an atomic number of 10 and an electron configuration of 1s² 2s² 2p⁶, magnesium must lose its two outermost electrons. By losing these 2 electrons, magnesium will have a total of 10 electrons, mirroring the electron configuration of neon.

Thus, magnesium must lose 2 electrons to achieve a filled outer shell, aligning its electron configuration with that of a noble gas. This tendency to lose electrons is characteristic of metals, which strive to attain stability by resembling the electron configurations of noble gases that precede them in the periodic table.