Two lines are perpendicular to each other if the product of their slopes is -1.

The given line is: \(2y - ax + 4 = 0\)

Let's first rearrange it to the slope-intercept form: \(y = \frac{a}{2}x - 2\)

The slope of the first line is: \(m_1 = \frac{a}{2}\)

The second line is: \(y + \frac{1}{4}x - 7 = 0\)

Rearranging it: \(y = -\frac{1}{4}x + 7\)

The slope of the second line is: \(m_2 = -\frac{1}{4}\)

For the lines to be perpendicular, their slopes must satisfy: \(m_1 \cdot m_2 = -1\)

Substitute the values of \(m_1\) and \(m_2\):

\(\frac{a}{2} \cdot \left(-\frac{1}{4}\right) = -1\)

Simplify:

\(\frac{-a}{8} = -1\)

Multiply both sides by -8:

\(a = 8\)