What is the
product of 2/3
and 4/5?

Well, product means multiply so we need to multiply these fractions.

2        4      
--- x ---  =  
3       5

now, when you are multipliying fractions you multiply the top and the bottom with the other one.
so 2 times 4 and 3 times 5 
and you get
8
--
15

since this fraction can not be simplifyed this is the final answer 8/15