How to align the rear derailleur?

Hey guys, I replaced my derailleur and cassette. I followed Calvin Jones’ tutorial for rear derailleur adjustment, but in 6th gear the chain touches the side of the cassette. If I rotate the barrel adjuster clockwise to move the chain toward the smallest cog, it then has a hard time shifting from 1st gear to 2nd gear. So it feels like a trade-off. Any idea how I can fix this?

Thanks