What number must be placed in the box in the equation below to produce an equation that has more than one solution:

\(\frac{1}{2}y + \frac{1}{4} = \frac{1}{12}\left(3+\boxed{\phantom{2}}~y\right)? \)

To get more than one solution, you want to create an identity; the same value on both sides of the equation.

I'm going to replace the box with the letter 'k'.

To make things simpler, multiply both sides by 12:

6y + 3 = 3 + ky

This shows that k must be 6.