Can she marry her mother’s half-brother?

Praise be to Allah.

The mothers brother is an uncle (khaal maternal uncle) whether he is a full brother or a half-brother through the father or mother. On this basis it is not permissible for you to marry him, because he is your uncle, may Allaah guide you. It is also haraam for a man to marry his maternal aunt (khaalah), because Allaah says (interpretation of the meaning): Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your fathers sisters, your mothers sisters [al-Nisa 4:23]. Similarly there is a total and eternal ban on women marrying their uncles. And Allaah knows best.