To determine the value of \( k \) in the equation \( x^2 + kx + 6 = (x + 2)(x + 3) \) for all \( x \), we can follow these steps:

Step 1: Expand the Right Side
We start by expanding the right-hand side of the equation:
- \((x + 2)(x + 3)\) can be expanded as:
\[
x^2 + 3x + 2x + 6 = x^2 + 5x + 6
\]

Step 2: Set the Equations Equal
Now, we equate the left side to the expanded right side:
- \( x^2 + kx + 6 = x^2 + 5x + 6 \)

Step 3: Compare Coefficients
Since the equation holds for all \( x \), we can compare the coefficients of \( x \) from both sides:
- The coefficients of \( x^2 \) are already equal.
- For the coefficients of \( x \):
\[
k = 5
\]
- The constant terms also match as both sides equal 6.

Conclusion
Thus, the value of \( k \) that satisfies the equation for all \( x \) is:
- \( k = 5 \)
This concludes the solution, confirming that the value of \( k \) is \( 5 \).