Step 1 :The volume of the solid formed by rotating a curve \(y=f(x)\) from \(x=a\) to \(x=b\) about the x-axis is given by the formula: \(V = \pi \int_{a}^{b} [f(x)]^2 dx\).
Step 2 :In this case, \(f(x) = e^{4x} + 6\), \(a=0\), and \(b=0.3\). We can use this formula to calculate the volume.
Step 3 :Substitute the values of \(f(x)\), \(a\), and \(b\) into the formula.
Step 4 :Calculate the integral to find the volume.
Step 5 :Final Answer: The volume of the solid formed by rotating the region enclosed by \(y=e^{4 x}+6\), \(y=0\), \(x=0\), \(x=0.3\) about the \(x\)-axis is approximately \(\boxed{18.849}\) cubic units.