Herein, we report a new concept for garnet materials in terms of the synthesis of nanocrystalline structure at low temperatures and its multimodal luminescence processes. Terbium- and ytterbium-ion-codoped yttrium gallium garnet nanophosphors have been synthesized via solution combustion technique; nearly pure phase nanophosphor samples were obtained. The synthesized nanophosphor shows efficient multimodal upconversion (UC), downshifting (DS), and quantum cutting (QC)/downconversion (DC) luminescence, which is a new paradigm in garnet material. The garnet nanophosphor shows strong green emission through DS and UC processes both. Furthermore, cooperative energy transfer (CET) has been described in detail, and a possible mechanism for the QC process is also proposed. A UV/blue photon absorbed by Tb3+ ion splits into two near-infrared photons (wavelength range 900-1040 nm), emitted by a Yb3+ ion pair, with an efficiency of more than 100%. The Yb3+ concentration dependent ET from Tb3+ to Yb3+ has been verified using time domain analysis. An ET efficiency as high as 28% and a corresponding QC efficiency of about 128% (for 15 mol % of Yb3+ concentration) have been attained. Such a multimode emitting nanophosphor could be very useful in display devices and for enhancing the conversion efficiency of next generation solar cells via spectral modification etc.