The reduction 4-octyne with \(H_2\) in the presence of \(Pd/CaCO_3\)-quindine gives

cis-4-octene

The correct answer is option 2. cis-4-octene.

When 4-octyne undergoes hydrogenation (reduction with \( H_2 \)) in the presence of a palladium catalyst (Pd) supported on calcium carbonate \((CaCO_3)\) and quinidine, the stereoselectivity of the reaction becomes crucial. Quinidine acts as a chiral modifier, influencing the stereochemistry of the hydrogenation process. Depending on the specific conditions and the geometry of the catalyst, quinidine can direct the hydrogenation to favor the formation of either cis- or trans-alkenes. In many cases, the hydrogenation of 4-octyne under these conditions predominantly yields cis-4-octene. The presence of quinidine in the catalyst system typically biases the hydrogenation process towards the cis-configuration of the resulting alkene. This results in the formation of predominantly cis-4-octene as the product.

Therefore, option (2) cis-4-octene is correct because in the reduction of 4-octyne with \( H_2 \) using \( Pd/CaCO_3 \)-quinidine as catalyst, the reaction typically yields cis-4-octene due to the stereoselectivity imparted by quinidine.