To solve this expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's simplify the division: 3/6 = 1/2.

Now, the expression becomes: -1/4 + 1/2 : 6.

Next, let's simplify the division: 1/2 : 6 = 1/12.

Now, the expression becomes: -1/4 + 1/12.

To add these fractions, we need a common denominator. The least common multiple of 4 and 12 is 12.

Converting -1/4 to have a denominator of 12: -1/4 = -3/12.

Now, the expression becomes: -3/12 + 1/12.

Adding these fractions, we get: -3/12 + 1/12 = -2/12.

Simplifying the fraction, we get: -2/12 = -1/6.

Therefore, -1/4 + 3/6 : 6 = -1/6.