What is the correct opening move in mancala when you go first in a 6 hole per side board?
This site suggests third-from-the-left (your 4) followed by far-right (your 1). 


  This opening has the following strengths:
  
  
  It empties bin F* early in the game, allowing Mi to play a single pebble from F into her mancala each time a single pebble lands there.
  It empties bin F at a time when at least two of the pebbles from F (those landing in J and I) will likely eventually come back around the board to Mi’s side.  Furthermore, if Yo makes the defensive G play, all five of the pebbles from G are ultimately likely to wind back up on Mi’s side.  For example, after playing G, Yo has six pebbles in H.  If she plays H on a subsequent turn, the sixth pebble in H will land in A, back on Mi’s side.
  It allows Mi to play from A, B, C, and F without repopulating Yo’s side of the board.  It therefore sets Mi up for an effective “starving” strategy. 
  Because of the large number of pebbles in each of Yo’s bins, it is unlikely that Yo will be able to counter with a stalling or starving strategy herself.
  Most importantly, it puts Yo in a defensive position at her very first move of the game.  Yo has an immediate glaring vulnerability to being raided in bin G, and must therefore seriously contemplate the defensive G or HG responses.  Either of these responses, however, leaves her in the weakened board position of having each of her remaining bins populated with enough pebbles to play around to Mi’s side, thus reinforcing a starving strategy by Mi.
  


They go into a considerable amount of detail explaining subsequent moves, analysis, and their conclusions: I would definitely recommend reading the entire page to understand it better.

*Note: this page labels your far-left bin A and continues counter-clockwise, so your far-right bin is F, your opponent's far-right bin is G, and your opponent's far-left bin is L. Yo is the opponent with the mancala on the left; Mi is the player with the mancala on the right.