  $IP$ sets play a fundamental role in arithmetic Ramsey theory. The Finite
Sums Theorem states that if we partition $\mathbb{N}$ into finitely many cells,
then atleast one cell is an $IP$-set. N.Hindman proved the Finite Sums Theorem
comboinatorillay in \cite{H}, which was a conjecture of Graham and Rothschild,
and an algebraic proof of the Finite Sums Theorem is followed from
\cite[Corollary 5.10]{HS}. In \cite[Theorem 2.6]{BH94} V. Bergelson and Hindman
combinatorially proved that for an additive $IP^{\star}$ set $A$ and any
sequence $\langle x_{n}\rangle_{n=1}^{\infty}$ there exists a sum subsystem
$\langle y_{n}\rangle_{n=1}^{\infty}$ of $\langle x_{n}\rangle_{n=1}^{\infty}$
such that $FS\left(\langle y_{n}\rangle_{n=1}^{\infty}\right)\cup FP
\left(\langle y_{n}\rangle_{n=1}^{\infty}\right)\subset A$. For multiplicative
$IP^{\star}$-set, an analogous study was made by A.sisto in \cite{S} using
algebra of the Stone-$\check{C}$ Compactification of $\mathbb{N}$ and he proved
that for any multiplicative $IP^{\star}$ set $A$ there exist some infinite
sequences $\langle x_{n}\rangle_{n=1}^{\infty}$ and $\langle
y_{n}\rangle_{n=1}^{\infty}$ of $\mathbb{N}$ such that $FS\left(\langle
x_{n}\rangle_{n=1}^{\infty}\right)\cup FE^{I}\left(\langle
x_{n}\rangle_{n=1}^{\infty}\right)\cup FP\left(\langle
y_{n}\rangle_{n=1}^{\infty}\right)\cup FE^{II}\left(\langle
y_{n}\rangle_{n=1}^{\infty}\right)\subseteq A$. In this article, we will
provide a combinatorial proof of the same result.
