Let us see. You first calculate the amount of dissolved oxygen in 294 ml of water which will be 8.6*294/1000 = 2.53 mg,
In the second step, calculate the O2 remaining in the 300 ml solution (remember the volume increases because you are adding waste water) 5.4*300/1000 = 1.62 mg
O2 used up by 6 mL of waste water = 2.53 - 1.62 = 0.91 mg
O2 required for 1 L of waste water = 0.91*1000/6 = 151.7 mg
so BOD5 of the waste water = 151.7 mg O2