Answer:
I have found and attached a spreadsheet (cities.xlsx) that matches this question.
First we remember the VLOOKUP sintax:
=VLOOKUP (lookup_value, table_array, col_index_num, [range_lookup])
We need to look up the City Type (B13),
compare it to the City/COL range (A7:B10),
and return the COL percentage (2nd column of City/COL)
so the VLOOKUP function on cell F13 has to be:
=VLOOKUP(B13,$A$7:$B$10,2)
Next, to multiply the result by the Total Base Lodging (B5):
=VLOOKUP(B13,$A$7:$B$10,2) *$B$5
Finally que copy the formula to the F14:F18 cells
Notice the use of $ to make cells static and avoid errors while copying the formulas to different cells.
I have attached the completed spreadsheet as "cities final.xlsx"