I believe that there are only two exocyclic bonds in this structure. But in some text its mentioned as three. can someone clarify.
By definition (in Woodward-Fieser rule), an exocyclic double bond is a double bond where one of the $sp^2$ carbon atoms of the bond is a part of a ring, while the other $sp^2$ carbon of the bond is not a part of same ring (it could be a part of another ring).
If both the $sp^2$ carbon atoms of the double bond is part of the same ring, then it is called endocyclic double bond. From these definitions, you can understand that exocyclic would stand for a double bond outside the ring and endocyclic would stand for a double bond within the ring. Following examples would illustrate the definition: