Fifteen plus, according to the latest war powers report to Congress. The uncertainty comes because the report says" approximately 90,000 United States Armed Forces personnel are deployed to North Atlantic Treaty Organization countries in Europe" without naming the countries. The conflicts are basically the same as in recent reports: Iraq, Syria, Yemen, Saudi Arabia, Jordan, Lebanon, Turkey, Somalia, Kenya, Djibouti, Niger, Cuba [at Guantanamo], Philippines, Egypt, and Kosovo plus NATO. The law requires reporting of places where troops equipped for combat are deployed; there does not have to be active combat.
I post this for consistency, not to make other judgments. I believe the war powers act has been a valuable tool for congressional oversight of military operations.