Let's simplify the given expression step by step.
The expression to be simplified is:
[tex]\[ 2 \sqrt{2} \cdot 7 \sqrt{18} \][/tex]
First, let's simplify the square root term:
[tex]\[ \sqrt{18} \][/tex]
Since 18 can be factored into 9 and 2, we have:
[tex]\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2} \][/tex]
Now, the expression becomes:
[tex]\[ 2 \sqrt{2} \cdot 7 \cdot 3 \sqrt{2} \][/tex]
Next, we'll multiply the constants and the square root terms separately:
[tex]\[ 2 \cdot 7 \cdot 3 \cdot \sqrt{2} \cdot \sqrt{2} \][/tex]
We know that:
[tex]\[ \sqrt{2} \cdot \sqrt{2} = \sqrt{4} = 2 \][/tex]
Thus, the expression simplifies to:
[tex]\[ 2 \cdot 7 \cdot 3 \cdot 2 \][/tex]
which can be computed as:
[tex]\[ 2 \cdot 7 = 14 \][/tex]
[tex]\[ 14 \cdot 3 = 42 \][/tex]
[tex]\[ 42 \cdot 2 = 84 \][/tex]
Therefore, the simplified form of the expression is:
[tex]\[ 84 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{84} \][/tex]
