The following frequency distribution's mode is:

Size of items	Frequency	Size of items	Frequency
0-4	5	20-24	10
4-8	7	24-28	6
8-12	9	28-32	3
12-16	17	32-36	1
16-20	12	36-40	0

For finding the mode of a grouped frequency distribution, we need to identify the modal class first.

Here, the maximum frequency is 17 and the corresponding class is $12-16$.

Hence, $12-16$ is the modal class.

We know that,

Mode $=l+\frac{f-f_1}{2f-f_1-f_2}\times h$

Where, $l\to$ lower limit of the modal class

$f\to$ frequency of the modal class

$f_1\to$frequency of the class preceding the modal class

$f_2\to$ frequency of the class succeeding the modal class

$h\to$class width

Here, $l=12,h=4,f=17,f_1=9$and $f_2=12$

$=12+\frac{17-9}{34-9-12}\times 4$

$\Rightarrow \text{ Mode }=12+\frac{8}{13}\times 4$

$=12+\frac{32}{13}$

$=12+2.46$

$=14.46$

Hence, the mode of the give frequency distribution is $14.46.$