  We study relations between unknotting number and crossing number of a spatial
embedding of a handcuff-graph and a theta curve. It is well known that for any
non-trivial knot $K$ twice the unknotting number of $K$ is less than or equal
to the crossing number of $K$ minus one. We show that this is extended to
handlebody-knots. We also characterize the handlebody-knots which satisfy the
equality.
