Hi Lan,
Let me see if I can help you. Farmboy was on the right track. First, the molecule (E)-4-octene is the hydrocarbon that is 8 carbons long and has a trans double bond between the C-4 and C-5 carbons. In other words, it's a symmetrical trans olefin with two n-propyl groups on each side of the double bond. The best way to synthesize a trans double bond is by performing a stereoselective reduction on the corresponding triple bonded compound, in this case, oct-4-yne. Two condtions that should work are the dissolving metal reaction conditons (Na metal / liq. NH3, -78 degrees C) or a lithium aluminium hydride reduction (LAH, THF). By the way, you could also try to get the olefin by doing a hydrogenation of the alkyne but it's very difficult to stop the reduction at the alkene state unless you use a poisoned catalyst. However, the problem with using a posinoned catalyst such as Lindlar catalyst is that the cis olefin is favored/formed.
The next part of the syntheis requires figuring out how to make oct-4-yne from compounds of 3 carbons or less. The best way is to do that is to react 1 equivalent of acetylene with 2 equivalents of propyl bromide in the presence of a strong base such as n-butyl lithium. If you add 2 eq. of BuLi to 1 eq of acetylene, you will get bis lithium acetylide [Li-C(triplebond)C-Li] which will undergo SN2 displacement of the alkyl halide to give you the desired alkyne...
Hope this helps!!!