As you see, each amino acid can be translated by one or more triplets. For example, Valine (Val) can be translated by the triplets GUU, GUC, GUA, GUG (5'-3' triplets of the mRNA).
Usually codons that are translating the same amino acid are grouped together to the same box (exept for serine and leucine, which can be translated by 6 different codons)
AUG translates Methionine and signals the start of protein synthesis.
Finally, 3 codons (UAA, UAG and UGA) are not translating any amino acid. They just signal the end of protein synthesis.
The letters at the purple boxes are showing the 1st, 2nd and 3rd base of the corresponding box. They just help you find the codon you are looking.
For the exercise: we already found that mRNA is AUGACGGAGGGGUAUUCUUAA (complementary to the DNA and with U instead of T)
Now we need to find out which is the 5' and which is the 3' end. We know that the ribosome "reads" the mRNA from 5' to 3'. So, the mRNA must have an AUG codon near the 5' end, and a stop codon (UAA, UAG or UGA) near the 3' end. Therefore, the mRNA stand is:
Then, you just use the chart to find the amino acids: