Prompt and nonprompt productions of exotic multiquark states are studied using the $\sim$10.4~fb$^{-1}$ data sample collected by the D0 experiment in Tevatron $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The recent D0 results on the prompt and nonprompt production of the $X(3872)$ and $Z_c^+(3900)$ states and the $P_c$ pentaquarks at the 4450~MeV region are reported. Signals corresponding to these states are found in the nonprompt production, whereas only the $X(3872)$ state is seen in the prompt production. The ratio of prompt to nonprompt $X(3872)$ production is about three times larger in the D0 measurement than that obtained by the ATLAS experiment at 8 TeV. Theoretically, the production, formation, coalescence, and disassociation processes are expected to be quite different for conventional mesons with a spatial size of (0.4-0.8) fm, compact multiquark states such as tetraquarks with a size of a few fm, and spatially extended molecular states with a size of (4-10) fm. They can be differently affected in prompt hadron-hadron collisions where there are many additional particles emitted from the interaction point. Consequently, the prompt to nonprompt production ratio of spatially extended exotic states can be suppressed at LHC comparing with the Tevatron conditions, because of large difference in the hadron-hadron collisions particle multiplicity. The prompt production studies provide an opportunity to better understand the nature of exotic states.