Grow lab 4x4 setup

I have purchased a growlab 4x4 a 6in blockbuster hood with a quantum dimmable ballast. I have purchased a 6in online fan and a phresh filter. My ? Is can I run my ventilation like this filter-ducting-hood-ducting-fan.

Yes, you can run it just fine like that.

might want to get a thermo stat for your fan depending on temps you run

also would do filter, fan, hood, order