You can multiply the fractions together to get the final answer. To multiply fractions you can times the top and the bottoms of both fractions together to get the new fraction;
1/2 * 2/3 = (1*2)/(2*3) = 2/6
Then you can simplify the fraction, to do this you can find a common number between the top and the bottom fractions and then you can divide the top and the bottom by that common number. In this case the common number between the two fractions is 2;
(2/2)/(6/2) = 1/3
The answer is 1/3,
Hope this helps! :)