Actually, there are 13 Eucharistic Prayers that one could encounter at present in the Roman Rite apart from the variants such as in the Anglican Use.
The four Eucharistic Prayers pictured above with the tabs I, II, III, and IV.
(Eucharistic Prayer IV, as already mentioned, has a fixed preface and the rubrics circumscribe when it may be used. The priest has latitude as to the use of the other three.)
Additionally, the tabs RI and RII above are the two Eucharistic Prayers for Masses of Reconciliation which were gifts to the Church by Blessed Paul VI on the occasion of the Holy Year 1975. There are rubrics which guide the priest in their selection.
There is the so-called Swiss Anaphora which has been approved for many years but which I find less used by the Americans for reasons I do not know; it is designated now as the Eucharistic Prayer for Various Needs and Occasion with four permutations and that prayer is seen in the photo above with the tabs above designated as VI, VII, VIII, and VIV…each version has its own theme and there are directives on the use.
Finally, there are the three Eucharistic Prayers for Masses with Children. With the third Editio Typica of the Roman Missal, it was mandated that these be published in a separate volume, and so they exist as a supplement. There are rubrics which guide the celebrant as to when these may appropriately be chosen.