The maximum number of basil plants you might have after thinning would
be 243.
Since the basil rows will be started 1 ft from the edges of the 10 ft
by 15 ft garden bed, the basil plants will be planted in a bed that is
8 ft by 13 ft. When you go in by 1 ft on each side you take off 2 ft
from the length and 2 ft from the width. The rows have to be planted
1 ft apart.
If you plant the rows horizontally (figure A), you will have 14 rows.
When the plants are thinned and are 6" apart, you will have 17 plants
in each row. The total number of plants will be 238 (14 x 17).
If you plant the rows vertically (figure B), you will have 9 rows.
When the plants are thinned and are 6" apart, you will have 27 plants
in each row. The total number of plants will be 243 (9 x 27).
So, planting the garden with 9 rows by 27 plants gives you the most
plants. You also have to make sure that you have enough seeds to
plant the garden this way. Each pack gives you 75 ft of seeds so 2
packs will give you 150 ft. If you have 9 rows that are 13 feet long
then you have a total length of 117 feet which means that you do have
enough seeds.