When trying to find synonyms for the phrase "impress forcibly", one can first consider what the phrase actually means. To impress forcibly means to make a strong or lasting impression on someone in a forceful or compelling way. Some synonyms for this phrase might include "forcefully impact", "impose upon", "enforce upon", "impress upon forcefully", or "compel to remember". Other options might include "ingrain upon", "embed within", or "cement within", depending on the context and specificity of the situation. Regardless of which synonym is used, the overall goal is to leave a strong and lasting impression on the person in question.