From set S, an integer is chosen and called s, and from set T an integer is chosen and called t. The product of the two integers s and t is called p. What is the total number of different values of p that can be determined in this way?

Take s = 1 and substitute all t value in p= st , so you get P = 1,2,3,6,8
similarly for s = 2 and all T ,P = 2, 4,6,12,16
for s = 3 and all T , P = 3, 6,9,18,24
for s = 4 and all T , P = 4,8,12,24,32
for s = 6 and all T , P = 6, 12,18,36,48

if you count different values of P you get the answer as 14