After verbs of preventing, quo minus (also written quominus) with the subjunctive means "from doing"; after a negative, quin can do the same job.
Verbs and phrases of hindering (obsto, impedio, prohibeo, deterreo, recuso, nihil obstat) take quo minus + subjunctive. It means literally "by which the less"; translate "from …ing": nihil obstat, quo minus hoc facias "nothing prevents you from doing this".
When the main verb is negative or has a negative sense, quin + subjunctive is used too: non impedio quin "I do not prevent (you) from"; non dubito quin "I do not doubt that"; fieri non potest quin "it cannot be that … not".
prohibeo can also take a plain infinitive: qui alba et nigra internoscere prohibet "which prevents (one) from telling white from black".
Quin at the start of a main clause is something else: "indeed, moreover", or in a question "why not?": Quin et animam considera "consider the soul too".