We find the probability of the complement event. (product < 6)

There are 2 ways they can choose different numbers. That is, each of the
ways one of them can choose a 1 and the other choose 2,3,4, or 5.  That's
2x4=8 ways. 

There are 2 ways they can both choose 1's or both choose 2's.

That's 8+2 or 10 ways to fail.

There are 10 ways for Alex to choose a number and 10 ways for
Winnie to choose a number.  That's 10x10 or 100 ways.

The probability of a failure is 10 ways out of 100, or 10/100 or 1/10.

So the probability of a success is 9/10.

Edwin