Given data

Electric field: $\vec E = 6\hat i + 5\hat j + 3\hat k \; \text{N/C}$

Surface area vector: $\vec A = 30\hat i \; \text{m}^2$

Since the surface lies in the $YZ$-plane, its area vector is along the $x$-axis, which is consistent with $30\hat i$.

Formula for electric flux

Electric flux through a surface is: $\Phi = \vec E \cdot \vec A$

Compute the dot product

$\Phi = (6\hat i + 5\hat j + 3\hat k) \cdot (30\hat i)$

Using dot product rules: $\hat i \cdot \hat i = 1, \qquad \hat j \cdot \hat i = 0, \qquad \hat k \cdot \hat i = 0$

Therefore, $\Phi = 6 \times 30 = 180$

Final answer

$\boxed{180}$

So the correct option is C.