hand down means give something used one (pass on to the next generation), or give a formal decision (e.g. I handed my necklace down to my little daughter. The government handed down ruling early morning.)

hand in means submit work for appraisal, or to give something (e.g. I have to hand in my resignation by the end of this month.)

hand (or give) something out means distribution, give to each person (e.g. We will hand out the materials at the meeting room.)

hand something over (to somebody) means to give (someone) the power or responsibility of something (e.g. The contractor had handed the facilities over to the company last year.)

hand up means to pass something to someone who is on a higher level. (e.g. Please hand this report up to managers.)

hang in means stay positive or not give up (e.g. Don’t give up, hang in there. I'm sure we'll be find.)

hang on means wait a short time, or hold tightly, or to continue doing something in difficult circumstances (e.g. Could you hang on for a moment till I’m free. Please hang on while the bus pulled off. The team hung on for victory.)

hang out means spend time relaxing, or socially (e.g. Instead of going to the party we are just going to hang out at my place. You still hang out in the pub.)

hang up means end a phone call (e.g. Ann didn't say goodbye before she hung up.)

hold back means not show emotion (e.g. I had to hold back my tears in front of the children.)

hold on means wear a short time (e.g. Please hold on while I transfer you to the Sales Department.)

hold onto means hold firmly as long as possible (e.g. Hold onto your money so you can buy some duty free gifts on the way back.)

hold up means to remain strong or successful, or delay when travelling. (e.g. Do you think his alibi can be held up (= continue to seem true) in court? I was held up by the terrible traffic and arrived an hour late for my appointment.)