To find the number of arrangements of at most 8 balls in a row, we need to consider the different possibilities based on the number of balls used.

Arrangements with 1 ball:
Since there are four different colors, we can choose any of the four colors for the single ball. Therefore, there are 4 arrangements with 1 ball.

Arrangements with 2 balls:
We can choose any two colors for the two balls. There are four options for the first ball and four options for the second ball. Therefore, there are 4 * 4 = 16 arrangements with 2 balls.

Arrangements with 3 balls:
We can choose any three colors for the three balls. There are four options for the first ball, four options for the second ball, and four options for the third ball. Therefore, there are 4 * 4 * 4 = 64 arrangements with 3 balls.

Arrangements with 4 balls:
We can choose any four colors for the four balls. There are four options for each ball. Therefore, there are 4^4 = 256 arrangements with 4 balls.

Arrangements with 5 balls:
We can choose any five colors for the five balls. There are four options for each ball. Therefore, there are 4^5 = 1024 arrangements with 5 balls.

Arrangements with 6 balls:
We can choose any six colors for the six balls. There are four options for each ball. Therefore, there are 4^6 = 4096 arrangements with 6 balls.

Arrangements with 7 balls:
We can choose any seven colors for the seven balls. There are four options for each ball. Therefore, there are 4^7 = 16384 arrangements with 7 balls.

Arrangements with 8 balls:
We can choose any eight colors for the eight balls. There are four options for each ball. Therefore, there are 4^8 = 65536 arrangements with 8 balls.

To find the total number of arrangements, we need to sum up the arrangements for each case:

4 + 16 + 64 + 256 + 1024 + 4096 + 16384 + 65536 = 87380

Therefore, the correct answer is option B) 87380.