Some synonyms for the phrase "give someone the runaround" include "evade," "dodge," "avoid," "sidestep," "distract," and "stonewall." These words all describe the act of deliberately avoiding giving a specific answer or providing information to someone who is asking for it. Giving someone the runaround can be frustrating and cause confusion, especially if the person being given the runaround needs a clear response or solution to the matter at hand. Therefore, it is important to be honest and forthright when dealing with others, and avoid playing games or giving them the runaround.