"You can run `8.0 m/s, 20%` faster than your brother"
This means when your brother runs 100m you can run 120m.
Your speed is 8m/s. Now we know that your brothers speed is `20%` less than your speed.
Speed of your brother `= 8-8xx20/100 = 6.4m/s`
Time required brother to run 150m `= 150/6.4s = 23.4375`
Time required to you to go 150m `= 150/8 = 18.75`
Head start for brother `= 23.4375-18.75 = 4.6825~=4.6`
So you need to give approximately 4.6 head start for brother.