To find the values of \( y \) where \(\sin y = \frac{\sqrt{3}}{2}\) within the interval \(0^\circ\) to \(360^\circ\), follow these steps:

1. Identify the Reference Angle:
\(\sin y = \frac{\sqrt{3}}{2}\) is a well-known value. The reference angle is \(60^\circ\), where \(\sin 60^\circ = \frac{\sqrt{3}}{2}\).

2. Determine the Quadrants:
- First Quadrant: \( y = 60^\circ \)
- Second Quadrant: Since sine is positive in both the first and second quadrants, we use the fact that the sine of an angle in the second quadrant can be found as \(180^\circ - \text{reference angle}\). So, \( y = 180^\circ - 60^\circ = 120^\circ \).

3. Verify the Range:
Both angles \(60^\circ\) and \(120^\circ\) lie within the specified range of \(0^\circ\) to \(360^\circ\).

Therefore, the correct values of \( y \) where \(\sin y = \frac{\sqrt{3}}{2}\) are:

D. 60°, 120°