As is well known, if $R$ is a Noetherian ring, then a finitely generated module over $R$ must be finitely presented. However, this is not necessarily true for coherent rings. For example, consider $k$ as a finitely generated module over $k[x_1,x_2,...]$ with infinitely many indeterminates, where $k$ is a field and $k[x_1,x_2,...]$ is a coherent ring. This module is not finitely presented, as demonstrated by the projective resolution of $k$: $$...\to k[x_1,x_2,...]\oplus\cdots\oplus k[x_1,x_2,...]\to k[x_1,x_2,...]\to k\to 0$$ In this resolution, the kernel of $k[x_1,x_2,...]\to k$ is $(x_1,x_2,...)$, which is not finitely generated.
Therefore, there are two questions:
On which rings must a finitely generated module be finitely presented?
Is there an 'if and only if' characterization for such rings?
If we are talking about left $R$-modules, the criterion is equivalent to $R$ being left Noetherian.
In fact, if $I$ is a left ideal, then $R/I$ is a finitely generated, hence finitely presented by assumption, which means that $I$ is finitely generated.