Finding the number of 1/6 in 2/3 involves dividing 2/3 by 1/6. To do this, we need to follow the steps below:

Step 1: Convert 2/3 to a fraction with a denominator of 6, which is the same as finding an equivalent fraction with a denominator of 6. To do this, we can multiply both the numerator and denominator of 2/3 by 2:

2/3 × 2/2 = 4/6

Step 2: Now we can divide 4/6 by 1/6. To do this, we can use the formula:

a ÷ b = a × 1/b

Where a is the numerator and b is the denominator. Substituting the values, we get:

4/6 ÷ 1/6 = 4/6 × 6/1 = 24/6

Step 3: Simplify the fraction 24/6 to its lowest terms by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6:

24 ÷ 6 = 4
6 ÷ 6 = 1

So, 24/6 simplifies to 4/1, which means there are 4 units of 1/6 in 2/3.

Therefore, the correct answer is option C, which is 4.