I think I may get it. The "recipe" is calling for you to make up a super-strong k-meta solution by adding 5 tsp of k-meta to 8 oz. of water. Then you take this strong solution and dole it into your juice/must at the rate of 1 tsp solution per gallon of must.
The math (shown below) works out to 5/48 of a tsp of dry k-meta powder per gallon of must. This works out to 5/8 tsp dry k-meta in a 6-gallon batch.
The math: There are 6 tsp in 1 US oz., so there are 48 tsp in 8 oz of water. So, if you take 1 tsp of the solution, you are taking 1/48 of the solution. Since there are 5 tsp of dry k-meta in the whole solution, you are taking 5/48 tsp of dry k-meta.