The correct answer is $\boxed{\frac{8}{3}\Omega}$.
To solve this, we can use the following formula for the equivalent resistance of three resistors connected in a triangle:
$$R_{eq} = \frac{1}{R_1 + R_2 + R_3}$$
In this case, we have $R_1 = R_2 = R_3 = 6\Omega$, so the equivalent resistance is:
$$R_{eq} = \frac{1}{6\Omega + 6\Omega + 6\Omega} = \frac{1}{18\Omega} = \boxed{\frac{8}{3}\Omega}$$
We can also solve this problem by considering the current that would flow through each resistor if a voltage were applied across the triangle. In this case, the current would be the same through each resistor, and the voltage drop across each resistor would be proportional to its resistance. Therefore, the equivalent resistance would be the reciprocal of the sum of the reciprocals of the resistances. This is the same as the formula above, but it can be helpful to think about it in terms of current and voltage drops.