When performing a dilation, the lengths from the center of dilation to the vertices of the original triangle are multiplied by the scale factor. In this case, the scale factor is 4 (from the notation \( DO,4 \)).
Since you are given that the length of line segment \( OB \) is \( \frac{3}{4} \), you can find the length of line segment \( OB' \) as follows:
\[ OB' = \text{Scale factor} \times OB \]
Substituting the scale factor and the length of \( OB \):
\[ OB' = 4 \times \frac{3}{4} \]
Calculating this gives:
\[ OB' = 3 \text{ units} \]
Thus, the length of \( OB' \) is 3 units.