In the fourth grade math, Mr. Zhang attended the commendation meeting. Four teachers need to shake hands, communicate and calculate. How many times did they shake hands? How many letters are they going to deliver? Shake hands, because shaking hands is mutual, shaking hands once means that two people shook hands. Suppose teacher Zhang shakes hands first, * * * three times at a time, and then shakes hands all over. Since everyone else has already shaken hands with Mr. Zhang, they only need to shake hands with the other two, and the last two shake hands once, so: 3+2+ 1=6.

Letters (not emails): Since everyone has to write letters, each teacher has to write three letters to the other three teachers, so the letters sent by the four teachers are 3*4= 12.