"Peut-être que le directeur voudrait me parler."

Translation: Maybe the director would want to talk to me.

[DOette]

Why is que needed here?

[Louradour5]

it's a phrasing structure, not a real explanation but : https://www.thoughtco.com/does-peut-etre-que-ubjunctive-1369264

Perhaps you came across this explanation, further in the exercice : https://forum.duolingo.com/comment/40064034

[Martyn413385]

Perhaps the director would like to talk to me - is also accepted