If your table is Source, and if NumberColumn has the number type, then this will work:
= Table.Group(Source, {"LetterColumn"}, {{"Column", each Text.Combine(List.Transform(_[NumberColumn], (x) => Number.ToText(x)), ","), type text}})
Table.Group does a group by operation, which creates a table made up of all of the rows with the same value in LetterColumn. _[NumberColumn] gives a list of the values in the NumberColumn column in this new table. The List.Transform part turns the numbers into text values, and Text.Combine joins those numbers together, with a comma separating each value.
If you need the surrounding quotes as well, you can do this:
= Table.Group(Source, {"LetterColumn"}, {{"Column", each """" & Text.Combine(List.Transform(_[NumberColumn], (x) => Number.ToText(x)), ",") & """", type text}})
"""" represents the " character, and & combines two text values.