When it comes to offering a helping hand, there are several synonyms for "hold out the hand" that can be used. One option is "extend a hand," which can be a more formal and polite way of saying the same thing. Another alternative is to "offer a hand," which can imply a sense of kindness or generosity. You could also use "proffer a hand," which has a slightly more formal and old-fashioned feel to it. Additionally, "reach out a hand" can be used to indicate an eagerness to lend assistance. Whatever synonym you choose, the important thing is to show that you are willing to help.