  We explicitly describe the K-moduli compactifications of log pairs formed by
a Fano complete intersection of hypersurfaces of fixed degree and a hyperplane,
by constructing an isomorphism with certain GIT quotients. We characterize all
possible GIT quotients of complete intersections of these hypersurfaces and
hyperplanes. Our main result is the first example of wall crossing for the
K-moduli of log pairs, where both variety and divisor admit deformations before
and after the wall. Furthermore, we explicitly describe the K-moduli of the
deformation family of Fano 3-folds 2.25 in the Mori-Mukai classification, which
can be viewed as blow ups of complete intersections of two quadrics in
dimension three.
  Our work uses the moduli continuity method for log pairs by relating the
K-moduli to certain GIT compactifications. In addition, we introduce the
reverse moduli continuity method, which allows us to relate GIT
compactifications to K-moduli of Fano varieties. We use explicit GIT methods to
classify in detail the GIT stability of a complete intersection of two quadrics
in dimension four together with a hyperplane section. We also classify the GIT
stability of a complete intersection of two quadrics in dimension three.
Furthermore, we explicitly compactify the moduli space of log Fano pairs of
complete intersections and hyperplane sections, by establishing a direct link
with GIT.
  We use the above methods to prove our main result, namely the explicit
description of the first wall crossing for the K-moduli of log Fano pairs, of
complete intersections of two quadrics in dimension four, and a hyperplane
section. The reverse moduli continuity method, alongside our computational GIT
techniques, allow us to compactify the K-moduli of the deformation family of
Fano 3-folds 2.25, which is one of the only three known explicit
compactifications of K-moduli of Fano threefolds.
