  Let $X$ be a simple normal crossing (SNC) compact complex surface with
trivial canonical bundle which includes triple intersections. We prove that if
$X$ is $d$-semistable, then there exists a family of smoothings in a
differential geometric sense. This can be interpreted as a differential
geometric analogue of the smoothability results due to Friedman,
Kawamata-Namikawa, Felten-Filip-Ruddat, Chan-Leung-Ma, and others in algebraic
geometry. The proof is based on an explicit construction of local smoothings
around the singular locus of $X$, and the first author's existence result of
holomorphic volume forms on global smoothings of $X$. In particular, these
volume forms are given as solutions of a nonlinear elliptic partial
differential equation.
  As an application, we provide several examples of $d$-semistable SNC complex
surfaces with trivial canonical bundle including double curves, which are
smoothable to complex tori, primary Kodaira surfaces and $K3$ surfaces. We also
provide several examples of such complex surfaces including triple points,
which are smoothable to $K3$ surfaces.
