Recall the definition of an Arrhenius base: a substance that increases the concentration of hydroxide ions (OH\(\textsuperscript{-}\)) when dissolved in water.
Examine each option to see if it produces OH\(\textsuperscript{-}\) ions in aqueous solution:
a) Mg(OH)\(\textsubscript{2}\) dissociates in water to give Mg\(\textsuperscript{2+}\) and 2 OH\(\textsuperscript{-}\) ions, so it fits the Arrhenius base definition.
b) BaO reacts with water to form Ba(OH)\(\textsubscript{2}\), which then dissociates to give OH\(\textsuperscript{-}\) ions, so BaO is also an Arrhenius base.
c) CH\(\textsubscript{3}\)NH\(\textsubscript{2}\) is a base but it does not produce OH\(\textsuperscript{-}\) directly; it is a Brønsted-Lowry base, not an Arrhenius base.