Introduction:
To find the distance between two parallel tangents of a circle of radius 6cm, we need to understand some basic concepts of circles and tangents.

Circle:
A circle is a closed figure in which all points on the circumference are equidistant from a fixed point called the center.

Tangent:
A tangent is a line that touches a circle at exactly one point.

Parallel Tangents:
Parallel tangents are two tangents drawn to a circle from an external point, such that they are parallel to each other.

Steps to find distance of two parallel tangents:

1. Draw a circle of radius 6cm and mark its center as O.
2. Draw a line passing through the center O and mark a point P outside the circle.
3. Draw a tangent to the circle passing through point P and mark the point of contact as A.
4. Draw another line parallel to the tangent at point A.
5. Draw a line passing through point P and parallel to the tangent at point A. Mark the point of contact with the circle as B.
6. Draw a perpendicular from the center O to the line AB and mark the point of intersection as C.
7. The distance between the two parallel tangents is equal to 2 times the length of OC.

Explanation:
When a perpendicular is drawn from the center of the circle to a tangent, it bisects the tangent at the point of contact. Therefore, in triangle OCA, OC is the perpendicular from the center of the circle to the tangent at A, and OA is the radius of the circle. Therefore, using the Pythagorean theorem, we can find the length of OC as:

OC = sqrt(OA^2 - AC^2)

Since OA = 6cm (given), we need to find the length of AC. In triangle APC, we have:

tan(angle APC) = AC/AP

Since angle APC is a right angle, we have:

tan(90) = AC/AP

Therefore, AC = AP (since tan of 90 degrees is undefined).

Now, we can find the length of AC as:

AC = sqrt(AP^2 - PC^2)

Since AP is the distance between the point P and the point of contact A, we have:

AP = PA = sqrt(OP^2 - OA^2)

Since OP is the distance between the center O and the point P, we have:

OP = sqrt(OA^2 + AP^2)

Substituting the values of OA and AP, we get:

OP = sqrt(6^2 + (sqrt(OP^2 - 6^2))^2)

Simplifying the equation, we get:

OP^2 = 36 + OP^2 - 36

Therefore, 36 is cancelled out and we get:

OP = 6√2

Now, substituting the value of OP in the equation for AC, we get:

AC = sqrt((6√2)^2 - 6^2)

Simplifying the equation, we get:

AC = 6√2

Now, substituting the values of OA and AC in the equation for OC, we get:

OC = sqrt(6^2 - (6√2)^2)

Simplifying the equation, we get:

OC = 6

Therefore,