Hey there!
The first thing you need to do is put your numbers in order from least to greatest:
16, 19, 23, 24, 25, 31, 37, 46, 47
Then, you need to cut the numbers into quarters. I would do this by finding the middle number or your mean, which is 25, then counting out to see which number is in the middle on either side. Your new groups that you have to find the middle number of are in brackets, and your middle number is bolded. Your lower quartile will be within the left/lower set of numbers.
[ 16, 19, 23, 24, ] 25, [ 31, 37, 46, 47 ]
The lower quartile would be the mean between 19 and 23, since that would split the lower group directly in half.
19 + 23 = 42
42 / 2 = 21
So, your lower quartile would be 21.
Hope this this was clear enough and helped you out! Feel free to ask me any additional questions if you have any. :-)