the product of 16 and c is increased by 6 to equal the qoutient 25 and 9. what is c?

Assuming 9 is the divisor and your information is accurate,

16c + 6 = 25/9

Multiply both ides by 9.

144c + 54 = 25

144c = 25 - 54 = -29

Divide both sides by 144.