If in `DeltaABC, angleB = 90^(@), AB = 6sqrt(3)` and AC = 12, find BC.

Answer

To solve the problem, we will use the Pythagorean theorem, which is applicable in right-angled triangles. In triangle ABC, angle B is 90 degrees, AB is given as \(6\sqrt{3}\), and AC is given as \(12\). We need to find the length of side BC.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- Let \(AB = 6\sqrt{3}\) (one leg)
- Let \(BC = x\) (the other leg)
- Let \(AC = 12\) (the hypotenuse)

2. **Apply the Pythagorean theorem**:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we can write:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the known values:
\[ 12^2 = (6\sqrt{3})^2 + x^2 \]

3. **Calculate the squares**:
- Calculate \(12^2\):
\[ 12^2 = 144 \]
- Calculate \((6\sqrt{3})^2\):
\[ (6\sqrt{3})^2 = 6^2 \cdot (\sqrt{3})^2 = 36 \cdot 3 = 108 \]

4. **Set up the equation**:
Now we can substitute these values back into the equation:
\[ 144 = 108 + x^2 \]

5. **Isolate \(x^2\)**:
To find \(x^2\), we rearrange the equation:
\[ x^2 = 144 - 108 \]
\[ x^2 = 36 \]

6. **Solve for \(x\)**:
Taking the square root of both sides gives:
\[ x = \sqrt{36} = 6 \]

7. **Conclusion**:
Therefore, the length of side \(BC\) is \(6\) units.

### Final Answer:
BC = 6 units.