Given that we need to find the equation of the circle whose centre lies on the positive y - axis at a distance of 6 from the origin and having radius 4.

Since the centre lies on the positive y - axis at a distance of 6 from the origin, we get the centre (0, 6).

We have a circle with centre (0, 6) and having radius 4.

We know that the equation of the circle with centre (p, q) and having radius ‘r’ is given by:

⇒ (x - p)² + (y - q)² = r²

Now we substitute the corresponding values in the equation:

⇒ (x - 0)² + (y - 6)² = 4²

⇒ x² + y² - 12y + 36 = 16

⇒ x² + y² - 12y + 20 = 0.

∴The equation of the circle is x² + y² - 12y + 20 = 0.