Why is 0.2 times 0.3 0.06?

you can write 0.2 as 1/5 and 0.3 as 3/10
and when you multiply 1/5 with 3/10 you get 3/50 ( multiply the numbers above and multiply the number below)
3/50=0.06

Or another way...

Convert the decimal fractions into whole numbers by multiply both by 10.

ie.

0.2 x 10 = 2

and

0.3 x 10 = 3

Now multiply together

2 x 3 = 6.

However, we have to remember that we multiplied both numbers by 10 (ie. 10 x 10 = 100) so we must remember to divide the answer by 100

...0.06

Why is 0.2 times 0.3 0.06?

You need to draw the pictures that I describe in order to understand what i am saying.

When you are multiplying numbers less than 1 you are best to think of the times sign as 'of'
for instance

1/2 * 1/2 = 1/2 of 1/2
And , if you have a half a cake and you eat half of it, then you will be eating 1/4 of the original cake. Draw a picture to see what I mean
1/2 *1/2 = 1/4
since 1/2=0.5 and 1/4=0.25 it follows that
0.5 * 0.5 = 0.25
I think for most people it is easier to think in fractions though.
--------------------------------------------------------
draw a long rectangular cake and break it into 10 pieces. each of those pieces is 1 tenth of the cake.
Now, you will need to split or imagine each of those 10 pieces split into 10 pieces to make a total of 10*10=100 pieces. Each tiny piece will be 1 hundreth of the cake.
Very lightly shade 3 tenths (0.3) of the cake. that's how much cake you started with. The rest is already gone. You have also shaded 30 hundredths (0.30) of the cake because 3/10=30/100

Yours question is 0.2 times 0.3 (0.2 of 0.3)
0.2 is 2/10 so you want

2/10 of the 30 tiny pieces of a cake that you have
1 tenth of 30 is 3
so 2/10 of 30 is 6
so the answer is 6 pieces of cake
but each piece is 1 hundreth of the original cake
so the answer must be 6 hundredths of the original cake
6 hundredths = 0.06

I hope that helps.