The point (6,7) means that x = 6 and y = 7 pair up together. Let's plug them into the inequality.
15*x + 11*y > 12
15*6 + 11*7 > 12 ... replace x with 6, y with 7
90 + 77 > 12
167 > 12 ... this inequality is true since 167 is larger than 12
Because the last inequality is true, this means the first inequality is true when (x,y) = (6,7).
Therefore, (6,7) is a solution to the inequality.