`DeltaABC` can be constructed in which `BC = 6cm, angleC = 30^(@) and AC - AB = 4 cm`.

Explanation

To construct triangle ABC with the given conditions, we will follow these steps:

### Step 1: Draw line segment BC
- Draw a line segment BC that measures 6 cm.

**Hint:** Use a ruler to measure and draw the line segment accurately.

### Step 2: Construct angle C
- At point C, construct an angle of 30 degrees using a protractor.

**Hint:** Place the protractor's center point at point C and mark the 30-degree angle.

### Step 3: Mark point A
- Let AC = AB + 4 cm.
- Since we do not know the lengths of AC and AB yet, we can express AB as x cm. Therefore, AC = x + 4 cm.
- We can place point A along the line that forms the 30-degree angle with point C.

**Hint:** You can choose a reasonable length for AB (x) to keep the construction manageable, ensuring that the lengths satisfy the triangle inequality.

### Step 4: Use the triangle inequality
- According to the triangle inequality, we need to ensure that AB + BC > AC.
- Since BC = 6 cm and AC = x + 4 cm, we can write:
- x + 6 > x + 4
- This simplifies to 6 > 4, which is always true.

**Hint:** Check that the lengths you choose for AB and AC satisfy the triangle inequality.

### Step 5: Measure and mark lengths
- Using a compass, measure the length of AB (x cm) and mark point A on the line you drew in step 3.
- Then, measure AC (x + 4 cm) from point A along the angle you constructed.

**Hint:** Ensure that your compass is set accurately to the lengths you need.

### Step 6: Connect points
- Finally, connect points A and B to complete triangle ABC.

**Hint:** Use a ruler to draw straight lines between the points accurately.

### Conclusion
You have now constructed triangle ABC with the given conditions: BC = 6 cm, angle C = 30 degrees, and AC - AB = 4 cm.

---