Thank you for the opportunity to help you with your question!
Let's remember that a synthesis reaction is the one at which two elements or compounds react to produce only an just only one product (it cannot be two or more products). The general formula is:
A + B ---------> AB
So then in our original exercise we have:
Cl2 + KI -----------> KCl + I2
So the right side would be the products. Then as we can see we have two products which are: KCl and I2 and that's why it is not a synthesis reaction because we have two products and we must have only one product so that it can be a synthesis reaction.
Please let me know if you need any clarification. I'm always happy to answer your questions.