If you double then triple a number, this is the same as cutting the number in half. What is the number?

Let N be the number...I assume you mean to double the number and take the product with it's triple???  ...If so, we have....... 

(2N)(3N) = (1/2)N        

6N^2 = (1/2)N 

12N^2  = N   .... subtract N from both sides

12N^2 - N = 0     factor

N(12N - 1)  = 0    so...N = 0  or N = 1/12