The phrase "thick hide" typically refers to someone who is emotionally resilient or tough-skinned. There are a number of words and phrases that could be used as synonyms for this term, including "thick-skinned", "resilient", "unyielding", "impervious", "unbreakable", "stoic", "indomitable" and "unflappable". Depending on the context, other words like "firm", "robust" or "sturdy" could also work. It's important to take into account the specific connotations and nuances of each word, and to choose a synonym that accurately conveys the intended meaning and tone.