To simplify the expression \( -34 - \sqrt{3} \cdot \sqrt{216} \), we first need to simplify \( \sqrt{216} \).
The prime factorization of \( 216 \) is: \[ 216 = 2^3 \times 3^3 \]
Taking the square root: \[ \sqrt{216} = \sqrt{2^3 \times 3^3} = \sqrt{2^2 \times 3^2} \times \sqrt{2 \times 3} = 6\sqrt{6} \]
Now substituting that back into the expression: \[ -34 - \sqrt{3} \cdot 6\sqrt{6} \]
We simplify \( \sqrt{3} \cdot 6\sqrt{6} = 6\sqrt{18} \). Now simplifying \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \]
Thus, \[ \sqrt{3} \cdot 6\sqrt{6} = 6 \cdot 3\sqrt{2} = 18\sqrt{2} \]
Putting it all together: \[ -34 - 18\sqrt{2} \]
As you can see, \( -34 - 18\sqrt{2} \) does not simplify to a whole number and is not one of the options given (48, 24, -48, -24).
Thus, if we are to check just the numeric parts disregarding \( \sqrt{2} \): The \( -34 \) would not directly match any of them without calculating \( -18\sqrt{2} \), so none of the numerical responses adequately fit.
If we evaluate the components of the question, none of the options represent the simplified form of the given expression. If a numeric result was meant, please confirm its nature or if additional context is required.