If Condition: Date comparison from two different tables

I would think that your column would go something along the lines of:

Column = 
MAXX(FILTER(ALL('Table B'),'Table B'[Start Date]>=[InProgressDate] && 'Table B'[End Date]<=[SolvedDate]),[Phase])

You can add column to your Table A like so:

let
    Source = TableA,
    #"Added Custom" = Table.AddColumn(Source, "Custom", each Table.SelectRows(TableB, (tblB) => tblB[StartDate] <= _[InProgressDate] and tblB[EndDate] >= _[SolvedDate])),
    #"Expanded Custom" = Table.ExpandTableColumn(#"Added Custom", "Custom", {"Phase"}, {"Phase"})
in
    #"Expanded Custom"

code in "Add-column"-dialogue: