In this exercise, you're going to be using both your thumb and index finger. Hopefully you've gotten beyond feeling any difficulties executing exercises 1 or 2, where you had a chance to work on each finger, individually. Now, you're going to alternate between the thumb and the index finger.
While this exercise is not particularily musical, the skills you are learning here will be very powerful. Eventually you will be fretting, picking different strings, and making really nice music - but for now, you just have to get your mind and body comfortable with the basic motions. Your fingers need to 'learn' where the strings are and how to make them sing.
I'd like to talk about 'drills' or 'exercises' for a minute, and try to justify the time I'm asking you to spend on this very lame exercise. We are charting a direct and dependable course for learning how to play music on your ukulele by fingerpicking. In order to play music, you need to have a physical command of the instrument. If you are trying to play music, but require concentrated effort to physically operate the instrument, that effort will stand in the way of music being produced. 'Exercises' or 'drills' are intended to teach each physical element of operating the instrument separately, so that that element will sink in as quickly and deeply as possible.
In this exercise, for example, you are learning to find and pluck a string with your index finger. Sounds easy, but through trying you can see how much dexterity is required - it is really easy to miss the string, hit a different string, or make a foolish little sound when you do pluck, or get your finger stuck in there. When you are concentrating on just that, it is easy to deal with the difficulty. If you were diving straight into a finger-picking song, you would be thinking about fretting the strings, which strings to pluck, which chord comes next, when thumb when finger - way too much stuff to just give your index finger a chance to get it all sorted out. Give your index finger a chance - the next exercise will demand a little autonomy from it.