The first thing you need to know is the date. Did you see a calendar on the wall in the betting cage? Look at the calendar to learn the date - Saturday 10th April 1937.
 

 
Macao's weather falls into 4 distinct seasons. Summer is from May until Mid-September, Autumn is from Mid-September to Mid-December, Winter is between Mid-December and March and Spring is from March to May.
 
The following chart from the US Naval Observatory Astronomical Applications Department details the exact lunar phases for the year 1937.
 
1937 Phases of the Moon
Universal Time
 
NEW MOON FIRST
QUARTER 		FULL MOON

LAST
QUARTER

     D      H   M      D      H   M      D      H   M      D      H   M
Jan 12 16 47 Jan 19 20 02 Jan 26 17 15 Feb 03 12 04
Feb 11 07 34 Feb 18 03 50 Feb 25 07 43 Mar 05 09 17
Mar 12 19 32 Mar 19 11 46 Mar 26 23 12 Apr 04 03 53
Apr 11 05 10 Apr 17 20 34 Apr 25 15 24 May 03 18 36
May 10 13 17 May 17 06 49 May 25 07 38 Jun 02 05 24
Jun 08 20 43 Jun 15 19 03 Jun 23 23 00 Jul 01 13 03
Jul 08 04 12 Jul 15 09 36 Jul 23 12 45 Jul 30 18 47
Aug 06 12 37 Aug 14 02 28 Aug 22 00 47 Aug 28 23 54
Sep 04 22 53 Sep 12 20 57 Sep 20 11 32 Sep 27 05 43
Oct 04 11 58 Oct 12 15 47 Oct 19 21 47 Oct 26 13 26
Nov 03 04 16 Nov 11 09 33 Nov 18 08 09 Nov 25 00 05
Dec 02 23 11 Dec 11 01 12 Dec 17 18 52 Dec 24 14 20
 
With the above information you should be able to select the correct options from the cashier's note and answer Li Tang's three questions.
 

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Note that you must have found the cashier's note or else Li Tang won't offer the correct options.