1. **State the problem:** We have a quadrilateral OPQR with side length 16 units. It is dilated by a scale factor of $\frac{3}{4}$ to form quadrilateral O'P'Q'R'. We need to find the length of side R'O'. 2. **Formula used:** When a figure is dilated by a scale factor $k$, each side length of the new figure is $k$ times the original side length. 3. **Apply the formula:** Original side length $= 16$ Scale factor $= \frac{3}{4}$ Length of side R'O' $= 16 \times \frac{3}{4}$ 4. **Simplify the multiplication:** $$16 \times \frac{3}{4} = \frac{16 \times 3}{4}$$ 5. **Cancel common factors:** $$\frac{\cancel{16} \times 3}{\cancel{4}} = 4 \times 3 = 12$$ 6. **Final answer:** The length of side R'O' is $12$ units.