How many quadrilaterals are there in the given figure ?

23

Quadrilateral means a 04 sided figure.

There are 09 quadrilateral in the figure, now we will combine them to find the remaining quadrilateral;

1&2, 3&4, 6&7, 8&9, 4&5, 6789, 345, 346, 5&7, 12345, 1234567, 3456789, 34567, and the big one 1 to 9. 

Therefore, there are total 09+14= 23 quadrilateral.