Let's simplify the given expression step-by-step:
[tex]\[
\frac{6}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{3}}
\][/tex]
First, simplify inside the radicals:
Multiply the two fractions:
[tex]\[
\frac{6 \cdot \sqrt{2}}{\sqrt{3} \cdot \sqrt{3}}
\][/tex]
Next, simplify the denominator:
[tex]\[
\sqrt{3} \cdot \sqrt{3} = 3
\][/tex]
So the expression becomes:
[tex]\[
\frac{6 \cdot \sqrt{2}}{3}
\][/tex]
Simplify the fraction:
[tex]\[
6 \div 3 = 2
\][/tex]
Thus, the simplest radical form of the expression is:
[tex]\[
2 \cdot \sqrt{2}
\][/tex]
This is the correct simplified form:
[tex]\[
\boxed{2 \cdot \sqrt{2}}
\][/tex]
