Word / formMeaning / explanation
التَّفَاخُرmutual boasting.
التَّعَارُفgetting to know one another.
التَّخَافُتwhispering privately to one another.
These are the textbook's examples of tafāʿul verbal nouns. تَعَارَفَ contains introductory tāʾ and medial alif, producing تَعَارُف; تَفَاخَرَ similarly gives تَفَاخُر.
Mutual action is conspicuous in these examples. Nevertheless, one should not assume that every tafāʿul verb always requires two explicitly named persons; usage and context matter.