看 is a hand (手, flattened on top) over an eye (目). It's the gesture of shading your eyes with your hand to LOOK into the distance — exactly what you do squinting at a far-off mountain. Hand + eye = to look.
看 is wonderfully flexible: 看书 (read a book), 看电视 (watch TV), 看朋友 (visit a friend), 看医生 (see a doctor). And remember 好 from week one? 好看 means 'good-looking' — the funFact promised you this. To say something looks good, you literally say it's 'good to look at'.
A hand (手) raised over the eye (目), shading it to LOOK far away.
好 + 看 = 好看 (good-looking). 好 + 吃 = 好吃 (delicious). 好 + 听 = 好听 (nice-sounding). 好 + any sense verb = 'good to [sense]'. You now hold the whole pattern.