  We obtain the basic $R$-matrix of the two-parameter Quantum group
$U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory
and determine its $R$-matrix with spectral parameters for the two-parameter
quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. Using
the Gauss decomposition of the $R$-matrix realization of
$U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$, we study the commutation relations of
the Gaussian generators and finally arrive at its $RLL$-formalism of the
Drinfeld realization of two-parameter quantum affine algebra
$U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$.
