I have asked this question before but I was not clear enough. I want to prepare a 37% w/w solution (in water)of sulfuric acid from 96% sulfuric acid. I need around 500ml, I know it won't be exactly that, I want to know how to use the conversion using density, I've been shown a way I think is incorrect and need some input.

You need w/w solution, so we assume

1. 96% is w/w to start,
2. density of water = 1 g/mL
3. volume of mixture equals sum of volumes (=> approximation).

We know that 500 mL of 37% w/w H2SO4 contains 500*0.37=185 g by weight of pure H2SO4.
Concentrated H2SO4 has a density of 1.842 g/mL, 96% has a slightly lower value.

1. Weigh x=500*0.37/0.96=192.71g of 96% sulphuric acid in an erlenmeyer.
2. Place water needed to dilute in a large beaker. Diluted mass is 0.96x/0.37 g. Therefore volume of water to dilute is approximately 0.96x/0.37-192.71/1.84=395.27 mL.
3. Add acid slowly into water, stirring constantly. When mixing is completed, rince erlenmeyer using diluted acid and add back to mixture. Stir.
4. Let mixture cool.

If better precision is required, reduce diluting water by 5%. When mixing is completed and cooled, top up with water to 0.96x/0.37 g (by weight). Stir.

Again, as you have been warned, know where the emergency shower and eye wash are located, wear goggles and lab coat, add acid to water very slowly while stirring, work in a fume chamber with fan on (concentrated H2SO4 fumes), clean up and label.