Running an application that needs 6 threads on dual core processor
If there are $2$ cores and $4$ threads, two threads will be assigned to each core. Similarly, if there are $6$ threads, three threads will be assigned to each core. For example, suppose $6$ threads are $T_1,T_2,T_3,T_4,T_5,T_6$. Then, say $T_1,T_2,T_3$ are assigned to core $1$ and $T_4,T_5,T_6$ are assigned to core $2$.
As you are saying, $T_1,T_2,T_3$ will switch back and forth on core $1$ to give an illusion of parallel. However, note that $T_1$ and $T_4$ are indeed running in parallel on different cores.