Synthesis of branched alkanes
@Radi: Critical changes to original post! I will guide you through a reasonable approach. You have to realize that you have not specified the stereochemistry of 11 -- of which there are 16 possible stereoisomers (8 racemates) -- but I will ignore the issue. You will recognize the symmetry in 3,4,7,8-tetramethyldecane (11), so we will look for a coupling reaction of two 7-carbon entities. (E)-2-Buten-1-ol (crotyl alcohol) (4) and triethylorthopropionate 5 are commercially available. The reaction of 4 and 5 is a Johnson-type Claisen rearrangement (Google it!) which produces racemic esters 7 via transition state 6. Reduction of the double bond of unsaturated esters 7 leads to saturated esters 8. Reduction of the ester group to an alcohol followed by conversion to a bromide gives structure 9. The Wurtz reaction (9 --> 11) is rarely used but here is an opportunity.
Alternatively, esters 8 under the same conditions of the Wurtz reaction produces the &alpha;-hydroxyketones 10 (acyloin condensation). While the Clemmensen reduction (10 --> 11) of aliphatic ketones does not work as well as with aromatic ketones, under these conditions you would lose both oxygens. If the ketone is produced (structure 10 less the hydroxyl group), a Wolff-Kishner reduction would lead to the tetradecanes (plural) 11.Read about these name reactions which will be of more value to you than your original proposal. Good luck!