State whether the following statements are True or False :
The product of two even numbers is always even.

Answer

To determine whether the statement "The product of two even numbers is always even" is true or false, we can follow these steps:

### Step 1: Understand what even numbers are
Even numbers are integers that are divisible by 2 without leaving a remainder. This means that when you divide an even number by 2, the result is a whole number.

**Hint:** Remember that even numbers can be expressed in the form of 2n, where n is any integer.

### Step 2: Write the expression for the product of two even numbers
Let’s denote two even numbers as 2a and 2b, where a and b are integers. The product of these two even numbers can be expressed as:

\[ (2a) \times (2b) \]

**Hint:** Think about how you can represent any even number mathematically.

### Step 3: Calculate the product
Now, let's calculate the product:

\[ (2a) \times (2b) = 4ab \]

**Hint:** Notice that 4ab can be factored to show that it is still divisible by 2.

### Step 4: Determine if the product is even
Since 4ab is a multiple of 2 (specifically, it is 2 times 2ab), we can conclude that the product is even.

**Hint:** Check if the result of your multiplication can be divided by 2 without a remainder.

### Step 5: Provide examples
To further confirm, we can take specific examples of even numbers:
- Example 1: 2 and 4
\[ 2 \times 4 = 8 \quad (\text{even}) \]
- Example 2: 6 and 12
\[ 6 \times 12 = 72 \quad (\text{even}) \]

**Hint:** Using specific numbers can help solidify your understanding of the concept.

### Conclusion
Since we have shown that the product of two even numbers is always even through both algebraic reasoning and specific examples, we can confidently state that the statement is **True**.

**Final Answer:** True