If Clarence already knew how to sing 6 pieces, and he expects to learn 1 new piece during each week of lessons, the number of lessons that she is going to know every week can be calculated as:
Y = 6 + X
Where X is the number of weeks and Y is the total number of pieces that she will know.
So, to find how many weeks of lessons will Clarence need before he will be able to sing a total of 8 pieces, we need to replace Y by 8 and solve for X, as:
8 = 6 + X
8 - 6 = 6 + X - 6
2 = X
Therefore, Clarence will need 2 weeks to be able to sing a total of 8 pieces.
Answer: 2 weeks