Brainline

Brainline is an uncredited 1970s game published by Berliner Spielkarten and Palitoy.

 BGG has this description of the rules:

A two player abstract game played on a 7 by 9 array of hexes. Each player has four pegs of his colour on the specified starting hexes. On his turn a player may move any one of his pegs any distance in a straight line but may not jump any other peg. The object of the game is to be the first to get all four pegs of your colour in a straight line. They do not have to be adjacent but there must be no opponent pegs between them.

I've also found this review in Games & Puzzles,