To find \(P(B \,|\, A')\), we use the formula for conditional probability:

\(P(B \,|\, A') = \frac{P(B \cap A')}{P(A')}\)

First, calculate \(P(A')\):

The total number of outcomes when throwing two dice is 36. The event \(A\) (sum less than 6) includes the outcomes: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1). There are 10 outcomes, so \(P(A) = \frac{10}{36}\).

Thus, \(P(A') = 1 - P(A) = 1 - \frac{10}{36} = \frac{26}{36}\).

Next, calculate \(P(B \cap A')\):

The event \(B\) (difference at most 2) includes outcomes where the difference between the numbers is 0, 1, or 2. The outcomes that satisfy \(B \cap A'\) are those that are not in \(A\) but satisfy \(B\). There are 16 such outcomes.

Thus, \(P(B \cap A') = \frac{16}{36}\).

Now, substitute these into the conditional probability formula:

\(P(B \,|\, A') = \frac{\frac{16}{36}}{\frac{26}{36}} = \frac{16}{26} = \frac{8}{13}\)