what sin does Hester commit in chapter 15, and why does she commit it

Yong Peal wants to know what the letter means on her mother's chest. Hester avoids telling Pearl the truth, insisting that she likes the gold stitching. Her sin is not telling the truth.

She doesn't tell Pearl the truth because she doesn't think it was a sin. The letter is a reflection of the sin that resulted in Pearl. Hester wishes to shield Pearl from this.