The answer is in the text. As has been said in the discussion, 1 tbsp (tablespoonful) is officially equivalent to 15 ml in the United States, and strange though it may seem it is officially recognised as a pharmaceutical unit in that country:

"15 mL = 15 cc = 3 tsp = 1 tablespoon (tbl or Tbsp)"
http://www.pharmacy.ca.gov/publications/measuring_liquid_med...

"1 1/3" means one plus one third: one and a third. One tablespoonful is 15ml, so a third of a tablespoonful is 5 ml, making 20 ml in all: this metric equivalent is given in square brackets in your text.

--------------------------------------------------
Note added at 21 mins (2014-03-26 09:38:04 GMT)
--------------------------------------------------

The abbreviation for millilitres can be written as ml or mL, but the latter is recommended, at least in the US. In any case, it should be separated from the figure: so 20 mL, or alternatively 20 ml, but not 20ml or 20mL.

--------------------------------------------------
Note added at 42 mins (2014-03-26 09:58:14 GMT)
--------------------------------------------------

Adding a note of explanation has unfortunately taken me from the front to the back of the queue :) Perhaps I should have left well alone!