  The current study explores the generalized embedded wormhole solutions in the
background of $f(\mathcal{R},\mathcal{G})$ gravity, where $\mathcal{R}$
represents the Ricci scalar and $\mathcal{G}$ denotes the Gauss-Bonnet
invariant. To investigate the necessary structures of the wormhole solutions we
thoroughly analyzed the energy conditions under $f(\mathcal{R},\mathcal{G})$
gravity within the anisotropic source of matter. To meet this aim, we consider
spherically symmetric geometry with the most generic gravity model of the
gravity. A modified version of the field equations is calculated for two
different embedded wormhole solutions. All the energy conditions are calculated
and shown graphically with the regional ranges of the model parameter. Further,
the invalid region of the energy conditions confirms the presence of exotic
matter. Finally, we have concluding remarks.
