There's at least two ways these paths are made - sprinkle and brushed.
In the first, a normal concrete path is made, but left a little sloppy. The stones are sprinkled over.
In the second, the stones are the ballast in the concrete and once half-set, the top is brushed off with a wet brush to reveal the stones.
Either way it was made, repairing it will be tricky and you may not ever match in completely.
Unfortunately, you haven't mentioned how the path is damaged or included any pics, so I can't advise you on how to repair. If it's more than a crack you'll need to source matching stones.
Crack, hole, stone erosion, half of it's disappeared down a mineshaft - what?