The figure shown is made up of rectangle ABCD, a circle with FG as the diameter, 2 identical small semi-circles with diameters EF and GH and 2 larger semi-circles with diameters EG and FH. The radius of the circle FG is 18 cm. EH is a straight line. The length of BC is 60 cm.

1. Identify the total length of the line segment EH

Since $ABCD$ is a rectangle and $EH$ is a horizontal line across it, the length of $EH$ is equal to the length of $BC$ (or $AD$).
$EH = BC = 60$ cm.

2. Express EH in terms of its segments

The line segment $EH$ is composed of $EF$, $FG$, and $GH$.
$EH = EF + FG + GH$

3. Use the given information to find EF

We are given that the radius of the circle $FG$ is $18$ cm, so its diameter $FG = 2 \times 18 = 36$ cm.
We are also given that the two small semi-circles are identical, so their diameters are equal: $EF = GH$.
Substituting these into the equation for $EH$:
$60 = EF + 36 + EF$
$2EF = 60 - 36 = 24$
$EF = 12$ cm.