Electric flux formula

Electric flux through a flat surface is $\Phi = \vec E \cdot \vec A = \vec E \cdot (A\hat n) = A(\vec E \cdot \hat n).$

Given data

$\vec E = \frac{2\hat i+6\hat j+8\hat k}{\sqrt 6}$ $\hat n = \frac{2\hat i+\hat j+\hat k}{\sqrt 6}$ $A=4\,\text{m}^2$

Compute the dot product

$\vec E \cdot \hat n = \left(\frac{2\hat i+6\hat j+8\hat k}{\sqrt 6}\right)\cdot \left(\frac{2\hat i+\hat j+\hat k}{\sqrt 6}\right)$

Multiply corresponding components: $\vec E \cdot \hat n = \frac{1}{6}(2\cdot 2 + 6\cdot 1 + 8\cdot 1)$ $= \frac{1}{6}(4+6+8)$ $= \frac{18}{6} = 3$

Now calculate flux

$\Phi = A(\vec E \cdot \hat n) = 4 \times 3 = 12$

Final answer

$\boxed{12\ \text{Vm}}$

Comparison with stored answer

Stored correct answer = $12$

Our derived answer also = $12$.

Hence, the stored answer is correct.