It happens periodically, and it’s happening again this year: next Friday, March 25 is both Good Friday and the Feast of the Annunciation.
What’s a Catholic to do?
The USCCB in its official calendar notes the following:
Since March 25, 2016 is Friday of the Passion of the Lord (Good Friday), the Solemnity of the Annunciation of the Lord, normally assigned to this day, is transferred to Monday, April 4, 2016. The Optional Memorial of St. Isidore, Bishop and Doctor of the Church, is omitted this year.
Which means: all the usual rules and obligations for Good Friday—abstinence, etc.—prevail.