Given:
- ABCD is a rhombus.
- The side length of the rhombus is 20 cm.
- Two angles of the rhombus are 60 degrees each.

To find:
The length of diagonal AC.

Solution:

Properties of a Rhombus:
1. All sides of a rhombus are equal in length.
2. Opposite angles of a rhombus are equal.
3. Diagonals of a rhombus bisect each other at right angles.
4. The diagonals of a rhombus are not equal in length.

Step 1: Find the Length of Diagonal BD
Since ABCD is a rhombus, the diagonals bisect each other at right angles. Therefore, we can divide the rhombus into four congruent right-angled triangles. Let's consider one of these triangles, such as triangle ABD.

In triangle ABD:
- The side AB is equal to half the side length of the rhombus, which is 10 cm.
- The angle ABD is 60 degrees.

Using the trigonometric function cosine, we can calculate the length of diagonal BD as follows:
cos(60) = AB / BD
BD = AB / cos(60)
BD = 10 / 0.5
BD = 20 cm

Step 2: Find the Length of Diagonal AC
To find the length of diagonal AC, we need to consider triangle ABC.

In triangle ABC:
- The side AB is equal to half the side length of the rhombus, which is 10 cm.
- The angle ABC is 90 degrees (since diagonals of a rhombus bisect each other at right angles).
- The angle BAC can be found using the property that the sum of the angles in a triangle is 180 degrees. Thus, angle BAC = 180 - 60 - 90 = 30 degrees.

Using the trigonometric function sine, we can calculate the length of diagonal AC as follows:
sin(30) = AB / AC
AC = AB / sin(30)
AC = 10 / 0.5
AC = 20 cm

Answer:
The length of diagonal AC is 20 cm.