To solve the given expressions, we need to simplify each one step by step. Let's go through each problem:

2) \(\sqrt{(4 - \sqrt{6})^2}\)

Since the square root and the square cancel each other out, we get:
\[ \sqrt{(4 - \sqrt{6})^2} = |4 - \sqrt{6}| \]
Since \(4 - \sqrt{6}\) is positive, we can drop the absolute value:
\[ 4 - \sqrt{6} \]

3) \(\sqrt{(3 - \sqrt{11})^2}\)

Similarly, the square root and the square cancel each other out:
\[ \sqrt{(3 - \sqrt{11})^2} = |3 - \sqrt{11}| \]
Since \(3 - \sqrt{11}\) is negative (because \(\sqrt{11}\) is approximately 3.32), we take the absolute value:
\[ \sqrt{11} - 3 \]

5) \(\sqrt{(10 - \sqrt{10})^2}\)

Again, the square root and the square cancel each other out:
\[ \sqrt{(10 - \sqrt{10})^2} = |10 - \sqrt{10}| \]
Since \(10 - \sqrt{10}\) is positive, we can drop the absolute value:
\[ 10 - \sqrt{10} \]

6) \(\sqrt{(\sqrt{3} - 2)^2}\)

Similarly, the square root and the square cancel each other out:
\[ \sqrt{(\sqrt{3} - 2)^2} = |\sqrt{3} - 2| \]
Since \(\sqrt{3} - 2\) is negative (because \(\sqrt{3}\) is approximately 1.73), we take the absolute value:
\[ 2 - \sqrt{3} \]

So, the simplified expressions are:
2) \(4 - \sqrt{6}\)
3) \(\sqrt{11} - 3\)
5) \(10 - \sqrt{10}\)
6) \(2 - \sqrt{3}\)