Solve the Fraction Equation: Finding the Number Plus 1/6 = 2/3

To solve this problem, we'll follow these steps:

• Step 1: Find a common denominator for the fractions involved.
• Step 2: Subtract $\frac{1}{6}$ from $\frac{2}{3}$ to isolate $?$.
• Step 3: Simplify the resulting fraction to find $?$.

Let's work through each step:
Step 1: The denominators are $6$ and $3$. The common denominator can be $6$ since it is the least common multiple of both numbers.

Step 2: Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of $6$. Multiply the numerator and the denominator by $2$ to get:

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Now the equation becomes:

$? + \frac{1}{6} = \frac{4}{6}$

Subtract $\frac{1}{6}$ from $\frac{4}{6}$:

$? = \frac{4}{6} - \frac{1}{6} = \frac{4 - 1}{6} = \frac{3}{6}$

Step 3: Simplify $\frac{3}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$:

$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

Thus, the value of the missing fraction $?$ is $\frac{1}{2}$.

The correct answer choice is $\frac{1}{2}$.