The image you uploaded contains a mathematical expression. The expression reads as follows:

$a) \, 2\sqrt{3} - \sqrt{2} + 2\sqrt{6} - 4\sqrt{3} - \sqrt{6} + 2\sqrt{2} + 4\sqrt{2}$

Let's simplify this expression by combining like terms.

Simplification:

1. Combine the $\sqrt{3}$ terms: $2\sqrt{3} - 4\sqrt{3} = -2\sqrt{3}$

2. Combine the $\sqrt{2}$ terms: $-\sqrt{2} + 2\sqrt{2} + 4\sqrt{2} = 5\sqrt{2}$

3. Combine the $\sqrt{6}$ terms: $2\sqrt{6} - \sqrt{6} = \sqrt{6}$

Now, put all the simplified terms together:

$-2\sqrt{3} + 5\sqrt{2} + \sqrt{6}$

This is the simplified form of the expression.

Would you like further details on how the simplification was done or have any other questions?

Related Questions:

1. How do you add and subtract terms involving square roots?
2. What are the rules for simplifying radical expressions?
3. How would you simplify an expression involving cube roots?
4. What happens if the square root terms do not have the same radicand?
5. How can you rationalize a denominator that involves a square root?

Tip:

When simplifying expressions with square roots, always look for like terms (terms with the same radicand) to combine them. This helps in reducing the expression to its simplest form.