  Usually, the three-tangle of a tripartite pure state of qubits can be
directly measured with the simultaneous preparation of a
not-less-than-four-fold copy of the state. We show that the exact genuine
tripartite entanglement for ($2\otimes2\otimes n$)-dimensional pure quantum
states can be measured in a similar manner, provided that only two simultaneous
copies of the state are available. Lower bounds are also proposed for more
convenient experimental operations. As an example, a comprehensive
demonstration of the scheme is provided for the three-tangle of a three-qubit
state.
