Summary: An equitable \(\underbrace{({\mathcal{O}}_k, {\mathcal{O}}_k, \ldots, {\mathcal{O}}_k)}_m\)-partition of a graph \(G\), which is also called an equitable \(k\) cluster \(m\)-partition, is the partition of \(V(G)\) into \(m\) non-empty subsets \(V_1, V_2\), \ldots, \(V_m\) such that for every integer \(i\) in \(\{1, 2, \ldots, m\}\), \(G[V_i]\) is a graph with components of order at most \(k\), and for each pair of distinct \(i, j\) in \(\{1,\ldots, m\} \), there is \(-1\leq|V_i|-|V_j|\leq1\). In this paper, we proved that every graph \(G\) with minimum degree \(\delta(G)\geq2\) and maximum average degree \(mad(G)<\frac{8}{3}\) admits an equitable \(\underbrace{({\mathcal{O}}_6, {\mathcal{O}}_6, \ldots, {\mathcal{O}}_6)}_m\)-partition, for any integer \(m\geq3\).