Option A: $x = 2$
Using the complementary event rule: $P(E) + P(\bar{E}) = 1$
$$\frac{x}{6} + \frac{2}{3} = 1 \implies \frac{x}{6} = 1 - \frac{2}{3} = \frac{1}{3} \implies x = 2$$
Source: Chapter 14, Section 14.1
The key formula is $P(E) + P(\bar{E}) = 1$. Substitute the given values and solve for $x$. Note that $\frac{2}{3} = \frac{4}{6}$, so $\frac{x}{6} = \frac{2}{6}$, giving $x = 2$. Don't confuse $x$ with $P(E)$; the question asks for the value of $x$, not the probability itself.