1. The problem is to find the value of $x$ such that $\cos x = 6$. 2. Recall that the cosine function, $\cos x$, has a range of values between $-1$ and $1$ for all real numbers $x$. 3. Since $6$ is outside the range $[-1,1]$, there is no real number $x$ for which $\cos x = 6$. 4. Therefore, the equation $\cos x = 6$ has no solution in the real numbers. 5. If considering complex numbers, solutions exist but require advanced methods beyond basic trigonometry.