To answer this question, we need to consider the worst-case scenario.
Let's assume that Mr. Brown picks gloves in such a way that he always selects gloves of a different color than the ones he has already picked. In this scenario, he would need to pick the maximum number of gloves without finding a matching pair.
Mr. Brown has 6 black gloves and 12 brown gloves. Since he wants to find a pair of the same color, he needs to pick the maximum number of gloves without finding a pair.
In the worst-case scenario, Mr. Brown would first pick a black glove, then a brown glove, then another black glove. At this point, he still does not have a pair of gloves of the same color.
Therefore, the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color is 3.
Option B) 3 - This option is correct because in the worst-case scenario, Mr. Brown will need to pick at least 3 gloves to find a pair of gloves of the same color.
The correct answer is B) 3.