Given data:
- Width of the block (b) = 10 cm
- Depth of the block (d) = 8 cm
- Length of the block (l) = 20 cm
- Depth of immersion (h) = 6 cm

Definition:
The metacentric height (GM) is the distance between the center of gravity (CG) of a floating body and its metacentre (M). It is used to determine the stability of a floating object.

Calculating the metacentric height:
1. The center of gravity (CG) of the block can be found by taking the average of the x, y, and z coordinates of its corners.
- x-coordinate of CG = (0 + b)/2 = b/2
- y-coordinate of CG = (0 + d)/2 = d/2
- z-coordinate of CG = (0 + l)/2 = l/2

2. The metacentre (M) is located at the center of buoyancy of the block when it is tilted slightly.

3. The center of buoyancy (CB) can be determined by considering the volume of the block that is submerged in water.

4. The volume of the submerged block can be calculated using the formula:
- Volume of the block = b * d * h
- Volume of the submerged block = Volume of the block - Volume above water level
= b * d * h - b * d * (l-h)/l
= b * d * (h/l)

5. The center of buoyancy (CB) is located at the centroid of the submerged volume, which is at a depth of h/2 from the waterline.
- x-coordinate of CB = b/2
- y-coordinate of CB = d/2
- z-coordinate of CB = h/2

6. The metacentric height (GM) is the vertical distance between the center of gravity (CG) and the metacentre (M).
- GM = z-coordinate of CG - z-coordinate of CB
- GM = (l/2) - (h/2)
- GM = (l - h)/2

Condition of equilibrium:
The stability of a floating object can be determined based on the position of the center of gravity (CG) relative to the metacentre (M).
- If the CG is above the M, the object is in stable equilibrium.
- If the CG is below the M, the object is in unstable equilibrium.
- If the CG coincides with the M, the object is in neutral equilibrium.

In this case, the metacentric height (GM) is positive, indicating that the CG is above the M. Therefore, the object is in stable equilibrium.

Summary:
- The metacentric height (GM) of the block is (l - h)/2, where l is the length of the block and h is the depth of immersion.
- The block is in stable equilibrium as the CG is above the M.