Looks right until near the end, assuming I've correctly guessed what the problem is! You didn't say what x, y, and z are (I initially guessed it was a notation for unit basis vectors i, j, and k, but eventually I realized they were given to you); and your notation is not good, using run-on equal signs and omitting parentheses.
But now look at your very last step. Why did you divide by -6? And does the resulting equation really say c = -44/6?
And you can check it yourself. Plug your value of c into the dot product equation, and confirm that you get 0. It won't work ...