"four people can be seated at a table. if two tables are put together, six people can be seated. how many tables are needed to make a long table that will seat 20 people? "

Am going to assume the table is four sided.
With one table, 4 people are able to seat, with 2 joined together 6 are able to seat.

For 20 people to be able to seat,  we first subtract the 2 persons seating opposite to each other.

20 - 2  =  18.

For each table 2 are seated on each table, to get number of tables, we divide the remaining 18 by 2.

= 18 / 2 = 9.
Therefore  9 tables would seat 20 people.