The mechanism of the reaction is as follows:
The first step is the supplementation of the acetate and the chalcone under basic conditions. The reaction is mentioned in the attachment.
The second step incorporates the reaction of the product from the first step to produce a cyclic product. This reaction goes through the Aldol mechanism. The reaction is mentioned in the attachment below.
Finally, the outcome produced in the above reaction goes through dehydration to produce a desired outcome. The reaction is mentioned in the attachment below.