Harry has 3 sisters and 5 brothers. His sister Harriet has S sisters and B brothers. What is the product of S and B?

First, in Harry's point of view: 3 sisters and 5 brothers

And, in Harriet's point of view: 2 sisters, (3-1), 6 brothers, (5+1)

So, the product of S and B is, \(S*B=6*2=\boxed{12}\).