This is a very important nuclear reaction that happens in red giant stars that have burned all their hydrogen so they start burning He instead. As stated by Jon Custer, the $^8$Be nucleus is unstable so its lifetime is short. At the temperature in a star, a lot of collisions between two alpha particles have the same energy as the Be nucleus with respect to two free alpha particles resulting in an efficient production due to resonance (the kinetic energy lies very close to the Gamow peak).
The density of He in the star is so high that the Be nucleus can collide with another alpha particle before decaying into two alpha's again. This process forms a nuclear excited state of carbon, which by accident, also has roughly the same energy with respect to the free particles as the collision energy of the particles in the star so that there is another resonance phenomenon. There is a small change that the Carbon atom decays to its ground state before falling apart in 3 alpha particles. This process is slow, but since it happens over cosmological time scales it is nevertheless very important and responsible for the formation of all elements heavier than lithium.
See also this explanation on the hyperphysics page.