Repeat the following procedure for the four given numbers.
Multiply the number by 12 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient.
The 1 st number is 2 . The result is
The 2 nd number is 6 . The result is
The 3rd number is 9 . The result is
The 4 th number is 11 . The result is
a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as $n$.
The result is $\square$. (Simplify your answer.)
b. Represent the original number as $\mathrm{n}$, and use deductive reasoning to prove the conjecture in part (a).
Multiply the number by 12 .
Add 12 to the product.
Divide the sum by 2 .
(Simplify your answer.)
Subtract 6 from the quotient.

Step 1 ：\(2 \times 12 = 24\)

Step 2 ：\(24 + 12 = 36\)

Step 3 ：\(36 \div 2 = 18\)

Step 4 ：\(18 - 6 = \boxed{12}\)

Step 5 ：\(6 \times 12 = 72\)

Step 6 ：\(72 + 12 = 84\)

Step 7 ：\(84 \div 2 = 42\)

Step 8 ：\(42 - 6 = \boxed{36}\)

Step 9 ：\(9 \times 12 = 108\)

Step 10 ：\(108 + 12 = 120\)

Step 11 ：\(120 \div 2 = 60\)

Step 12 ：\(60 - 6 = \boxed{54}\)

Step 13 ：\(11 \times 12 = 132\)

Step 14 ：\(132 + 12 = 144\)

Step 15 ：\(144 \div 2 = 72\)

Step 16 ：\(72 - 6 = \boxed{66}\)

Step 17 ：Let the original number be \(n\)

Step 18 ：Multiply the number by 12: \(12n\)

Step 19 ：Add 12 to the product: \(12n + 12\)

Step 20 ：Divide the sum by 2: \((12n + 12) \div 2 = 6n + 6\)

Step 21 ：Subtract 6 from the quotient: \(6n + 6 - 6 = \boxed{6n}\)