The slang expression 420 originated in California in the 1970's when students would meet outside their school at 4:20 p.m. and smoke weed. In contemporary culture 420 refers to April 20 when at 4:20 p.m. pot smokers light up in celebration of marijuana use. Teenagers often use 420 as a replacement word for weed.
Sixty-nine means giving your partner oral sex while your partner is giving oral sex to you at the same time. And so you're also both receiving oral sex from each other. Oral sex is when people use their mouths to stimulate another person's genitals.