Carbon decrease from 1-octyne to 1-hexene I am to turn 1-octyne to 1-hexene. 

Method 1



1) Reduction using sodium metal in pure ammonia to an alkene. 

2) Halohydrin formation; the -OH installs at the more substituted carbon due to its greater ability to stabilize positive charge (this always confused me; the more substituted carbon is both more positive in character and has more electron-donating methyl groups?)

3) Conversion of OH to a good leaving group (-OTs) using a sulfonate ester and a weak base, pyridine. 

4) E2 elimination using NaOH and heat. Because of resonance and sheer bulk and negative induction the OTs(-) should make for a better leaving group than Br-. So the internal alkene is formed. 

5) Two-part one step ozonolysis; creation of aldehyde. 

6) Reduction of carbonyl with hydrogen and transition metal to terminal alcohol.

7) Conversion of terminal alcohol to a better leaving group using tosyl chloride and pyridine again. 

8) Use of LDA to deprotonate and create the terminal alkene. 

Method 2

Also we can take another route with the brominated alkene; we can use OsO4 and basic hydrogen peroxide to create a 1,2 (vic) diol, which can be cleaved by periodic acid, and this creates a primary alcohol, which we convert to a good leaving group using tosyl chloride and pyridine, and we can eliminate. Same number of steps, but just something different that I thought of. Well, perhaps slightly simpler since there isn't a need for a two-step process (ozonolysis).
In principle, this can be realized in two steps:


Oxidative cleavage using catalytic amounts of $\ce{RuO2}$ and excess of oxone converts 1-octyne to heptanoic acid. (DOI)
Heating a mixture of acetic anhydride and a carboxylic acid in the presence of $\ce{Pd}$ catalyst turns the acid to a terminal alkene lacking one carbon atom (DOI). Admittedly, the high temperatures needed might be a problem here and may force you to perform the reaction in a sealed tube in an autoclave.