The DNA template strand of a gene near a promoter reads 5'-TAGAACGCCTCGAAATTTCATACT-3' The amino terminus of the encoded protein whose translation starts in this region is:

The N-terminal aminoacid is Metionin.

Explanation:

Before answering the question, let us remember the meaning of the term amino terminus. Terminus refers to the extremes of the polypeptide. During translation, rRNA and tRNA read mRNA in 5´ to 3´ direction. The first extreme to be translated carries the amino-terminal group, while the other extreme carries the carboxy-terminus group.

Conventionally, proteins are written from left to right, beginning by the N-terminal extreme carrying the free amine group, and ending by the C-terminal extreme carrying the carboxyl free group. However, we need to know that the free amine group actually places at the end of a protein.

Transcription:

Transcription occurs in the nucleus where the template DNI strand is read in direction 3´→ 5´ to build the mRNA molecule in direction 5´→ 3´.

template DNI strand  ⇒   5'-TAGAACGCCTCGAAATTTCATACT-3'

                      mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

Translation:  

Translation occurs in the cytoplasm. rRNA and tRNA read mRNA in the direction 5´→ 3´ to build the protein.

Protein synthesis initiates in the AUG start codon -Metionin-, and ends when reaching either of the stop codons UAA, UAG, UGA.  

The first portion of mRNA is not read nor translated. This is the untranslated region (UTR), placed before the strat codon.

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

Remember that transcription occurs from 5´ to 3´ extremes, so we need to read the codons in this direction too, beginning on the 5´ extreme.

First, we need to find the initiation codon: AUG coding for Metionin.

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                                                        Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                                                Lys  Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                                        Phe   Lys  Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                                 Arg  Phe  Lys  Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                        Gly  Arg  Phe  Lys  Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                                Val  Gly  Arg  Phe  Lys  Met

mRNA   ⇒  3´-AUCUUGCGGUGCUUUAAAGUAUGA- 5´

                       Leu  Val  Gly  Arg  Phe  Lys  Met

The N-terminal aminoacid is then Metionin.

weathering is the answer.