Draw a line segment AB=7.8 and by a ruler and compass obtain a line segment of length of 3/4(AB).

HINT:3/4*7.8

Here, we are given that $AB=7.8$. We need to obtain a line segment which measures $\frac{3}{4}\left(AB\right)$.
Now, we know that $AB=7.8$.
So,
$$\begin{gathered} \frac{3}{4}\left(AB\right)=\frac{3}{4}\left(7.8\right) \\ \frac{3}{4}\left(AB\right)=5.9 \end{gathered}$$

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Use the following steps of construction to obtain the required line segment.
1) Draw a line segment $AB=7.8$.
2) With A as centre and radius equal to 5.9 ($\frac{3}{4}\left(AB\right)$), draw an arc.
3) Mark the point of intersection of the arc with the line as C.
4) AC is the required line segment.

Thus, AC is the required line segment which measures $\frac{3}{4}\left(AB\right)$