1

This is the version of the question WHICH DOES USE KEY SIGNATURES.  

2

The first step is easy. Just write out each note-head a 3rd  lower - i.e.  one line below (if a line note) or one space below ( if  a space note). Leave a space at the beginning after the clef to add the key signature in step 2 and before each note-head to add accidentals in step 3.

Work out the key (scale) of the extract.  Knowing your cycle of 5ths, a key signature of 2 flats means either Bb major, or G minor.  Although there are accidentals, and one F#, the tune is centred around the Bb major chord at the beginning, and there are more F naturals than sharps so the key is  Bb major.  A minor 3rd down from Bb is G so the transposition will be written in G major.  (Not G minor - don’t  get fooled  into thinking the transposed scale is minor scale because the transposing interval is a minor interval.   Transposition will never change a  piece from major to minor or from minor to major.)  Knowing the key signature of G major is one sharp  - F# - add the key signature.

( If you had determined the original  as G minor, the same reasoning would have lead to the transposed key of E minor also with one sharp - it’s not the end of the world if you get the major/minor determination wrong.)

3

Because we have worked through key signature,  accidentals are going to be needed only where accidentals were used in the original but it could be a different sort of accidental.  In this case E natural accidentals become C# accidentals.

4

Double -check key notes of the original scale - e.g. tonic and dominant -  have been treated correctly.

In this case Bb’s have become G’s and F’s have become D’s.