"Sie versteht nicht, warum er nicht mit ihr tanzen möchte."
Translation:She does not understand why he does not want to dance with her.
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"Möchte" means "would like," more or less the same as "want." It's "mögen/mag" that means to "like" something (and "möchte" is the subjunctive of that verb).
"Why he does not like to dance with her" actually wouldn't use either of those though; it would be "warum er nicht gerne mit ihr tanzt."