Step 1: Find the rate of growth

The rate of growth of the plant with respect to sunlight is given by the derivative of $y$ with respect to $x$.

Step 2: Differentiate the equation

Differentiate $y = 4x - \frac{1}{2}x^2$ with respect to $x$:

$\frac{dy}{dx} = \frac{d}{dx}(4x - \frac{1}{2}x^2) = 4 - x$

So, the rate of growth of the plant with respect to sunlight is $4 - x$ cm/day.

Step 3: Find the number of days to attain maximum height

To find the number of days when the plant attains its maximum height, we need to find when the rate of growth is zero, i.e., $\frac{dy}{dx} = 0$.

Step 4: Solve for x

Set $4 - x = 0$, which gives $x = 4$ days.

Step 5: Find the maximum height

Substitute $x = 4$ into the original equation to find the maximum height:

$y = 4(4) - \frac{1}{2}(4)^2 = 16 - \frac{1}{2}(16) = 16 - 8 = 8$ cm.