1. **State the problem:** Find the area of the irregular polygon with given side lengths 6 cm, 2 cm, 8 cm, 3 cm, 5 cm, 2 cm, 2 cm, and 8 cm. 2. **Analyze the figure:** The shape can be decomposed into simpler shapes: a large rectangle, a left triangular protrusion, and a small right rectangular step. 3. **Calculate the area of the large rectangle:** The rectangle has length $8$ cm and height $6$ cm. $$\text{Area}_{rectangle} = 8 \times 6 = 48$$ 4. **Calculate the area of the left triangular protrusion:** The triangle has base $2$ cm and height $2$ cm. $$\text{Area}_{triangle} = \frac{1}{2} \times 2 \times 2 = 2$$ 5. **Calculate the area of the small right rectangular step:** The step has length $3$ cm and height $2$ cm. $$\text{Area}_{step} = 3 \times 2 = 6$$ 6. **Sum all areas:** $$\text{Total area} = 48 + 2 + 6 = 56$$ 7. **Final answer:** The area of the figure is $56$ square centimeters.