find probability that (a)Both are White (b)Both are black

A Teaching Method

Set up a six by eight table as a "sample space".
Mark the top axis (6 squares) WWWWBB for the first bag.
Mark the vertical axis (8 squares) WWWBBBBB for the second bag.
Now mark each square in the table as a conjoint event WW, WB etc

Each question can be answered by counting the squares for that conjoint event and stating that total as a fraction out of 48.

P(w1) = 4/6
P(b1) = 2/6
P(w2) = 3/8
P(b2) = 5/8

P(w1 and w2) = P(w1) * P(w2)
P(b1 and b2) = P(b1) * P(b2)
P(w1 and b2 or w2 and b1) = P(w1) * P(b2) + P(w2) * P(b1)