Notice that the quotient of 15.86 divided by 0.65 is written as the following devision:
15.86 / 0.65
This is the same as if we multiply both numerator and denominator by 100 and get:
1586 / 65
Now, we see that these two numbers are multiples of 13, so a factor of 13 can be extracted from them:
1586 = 13 * 122
65 = 5 * 13
Then (after simplifying the factor 13 from numerator and denominator) our quotient was reduced to:
122/5
and this quotient is much simpler to obtain without the use of a calculator (which is what I suspect your teacher wanted you to do):
5 enter into 12 2 times, you carry a 2 to the column of the units and examine how many time 5 enters in 22 (answer is 4), and end with 20 divided by 5 in the decimal section (after the decimal point), which gives 4:
Then continuing with the division we get:
1586 / 65 = 122 / 5 = 24.4