كَمْ ضَرْبَةً ضَرَبْتَ؟
كَمْ: indicates the number of occurrences of the action and occupies a cognate-object function.
ضَرْبَةً: the accusative tamyīz, specifying the unit being counted.
ضَرَبْتَ: past verb with tāʾ as subject.
The syntactic position of kam and the visible ending of ḍarbah are two distinct questions.