If A is a square matrix of order 4 and |A| = 4, then |2A| will be:

The correct option is 64.

To find the determinant of the matrix $\left|2A\right|$, we can use a fundamental property of determinants for square matrices.

For any square matrix $A$ of order $n$ and any scalar $k$, the determinant of the scalar multiple of the matrix is given by the formula:
$\left|kA\right|=k^n\left|A\right|$

In this problem, we are given the following values:
- The order of the square matrix $A$ is $n=4$.
- The determinant of matrix $A$ is $\left|A\right|=4$.
- The scalar value is $k=2$.

Substituting these values into the formula, we get:
$\left|2A\right|=2^4·\left|A\right|$

Calculating the exponent:
$2^4=16$

Now, substitute this back and multiply by the determinant of $A$:
$\left|2A\right|=16·4=64$

Therefore, the value of $\left|2A\right|$ is 64.