A projectile nucleus P (α-particle, mass number 4, total binding energy 28.0 MeV) strikes a stationary target nucleus T (mass number 12, total…

The $Q$-value is the increase in total binding energy of the products over the reactants: $Q=114.0-(28.0+92.0)=-6.0\ \mathrm{MeV}$, so the reaction is endothermic. At threshold the products move together with the velocity of the centre of mass, so the kinetic energy available for the reaction is only the kinetic energy in the centre-of-mass frame, which must equal $|Q|$. In the laboratory frame $K_{cm}=K_{lab}\dfrac{m_T}{m_P+m_T}$. Setting $K_{cm}=|Q|$ gives $K_{th}=|Q|\,\dfrac{m_P+m_T}{m_T}=6.0\times\dfrac{4+12}{12}=8.0\ \mathrm{MeV}$. A common mistake is to take the threshold equal to $|Q|$ itself, which ignores the kinetic energy that must be retained by the moving centre of mass.