The reactions proceed as follows:
Step 1: In the first step, \(\text{KOH (alc.)}\) induces an elimination reaction, which removes a bromine atom from the carbon chain, resulting in the formation of cyclooctene (a 8-membered ring with a double bond).
Step 2: The second step with \(\text{NaNH}_2\) induces further elimination, removing another hydrogen atom from the carbon-carbon single bonds (a step leading to the formation of cyclooctyne, a 8-membered ring with a triple bond).
Step 3: The reaction with \(\text{Hg}^{2+}/\text{H}^{+}\) induces hydromercuration of the alkyne, resulting in the addition of a mercury ion to the carbon-carbon triple bond.
This creates an alkene intermediate.
Step 4: Finally, the Clemmensen reduction with \(\text{Zn-Hg} / \text{H}^{+}\) reduces the alkene to a fully saturated ring, cyclooctane, which is the final product.
This reaction removes the double bond and saturates the 8-membered ring.