The given expression is \( 2\sqrt{14} \times (-3\sqrt{2}) \).

Let's break this down step by step:

1. Multiply the constants:  
   \( 2 \times (-3) = -6 \)

2. Multiply the square roots:  
   \( \sqrt{14} \times \sqrt{2} = \sqrt{14 \times 2} = \sqrt{28} \)

Now, simplify \( \sqrt{28} \):
- \( \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7} \)

So the full expression becomes:  
\[
-6 \times 2\sqrt{7} = -12\sqrt{7}
\]

Thus, the simplified result is \( -12\sqrt{7} \).

Do you want further details, or do you have any questions?

Here are 5 related questions:
1. How do you multiply two square roots in general?
2. Can all square roots be simplified further?
3. What are the rules for multiplying terms with square roots and constants?
4. How do we simplify expressions with radicals in denominators?
5. What are common mistakes made when multiplying radicals?

**Tip:** Always check if square roots can be simplified before multiplying them—it can make your calculations easier.

Learn how to multiply radicals in the expression 2√14 × (-3√2) with a step-by-step solution. This problem involves multiplying constants and simplifying square roots, resulting in -12√7. Suitable for students in Grades 9-10.

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