The German verbs zwingen and erzwingen look very similar (especially in the past tense as gezwungen and erzwungen) and have similar meanings, but there are some fine points in distinguishing their proper usage. Let's take a look first at some examples of zwingen:
Na ja, es wird sicher kein Problem sein,
Well, it will certainly not be a problem
den Internetbetreiber zu zwingen, den Film zu löschen.
to compel the internet provider to delete the movie.
Captions 6-7, Die Pfefferkörner - GerüchteküchePlay Caption
Und wir waren gezwungen, einige Kürzungen vorzunehmen.
And we were forced to make some cuts.
Caption 14, Berufsleben - Probleme mit MitarbeiternPlay Caption
Es ist aber auch keine Mutter jemals gezwungen worden
There, indeed, has never been a mother [who was] forced
im Fortuna-Kreißsaal zu entbinden.
to deliver in the Fortuna delivery room.
Captions 34-35, Fortuna Düsseldorf - Kreißsaal für FußballfansPlay Caption
Thus, the verb zwingen refers to the person or company etc. that is being forced or compelled to do something.
The verb erzwingen is also usually translated as "to force" or "to compel," as well as "to enforce," but with erzwingen it is not about who is being forced, but what is actually being enforced, be it a situation, arrangement, or law etc.
Er hat die Entscheidung erzwungen.
He forced the decision.
Sie erzwingt ein Versprechen.
She is forcing a promise to be made.
An easy way to remember the difference between the two verbs is that zwingen is always about who is being forced or compelled to do something, and erzwingen is always about what is being forced, compelled, or enforced upon somebody:
Die Regierung wurde gezwungen, die neuen Gesetze zu erzwingen.
The government was compelled to enforce the new laws.
Search for more examples of zwingen in its various conjugations on Yabla German and try writing some sentences on your own using both verbs.