Final answer:
The product of (-2/3) and (1/6) simplifies to -1/9 after multiplying the numerators and denominators and simplifying the fraction, corresponding to option a) -1/9.
Step-by-step explanation:
The calculation in question is finding the product of two fractions, which is basic arithmetic involving negative numbers and fractions. In this case, we have (-2/3)(1/6). Multiplying the numerators together, -2 times 1 gives us -2, and multiplying the denominators together, 3 times 6 gives us 18. Therefore, the product in fraction form is -2/18, which can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
So, the simplified fraction is -1/9, which corresponds to option a) -1/9.