There are several aspects of Hume's philosophy which are relevant here.
Firstly, in general tenor he was sceptical and has been regarded as an eminent and early positivist (before that term was
invented).
Secondly, the distinction between "relations of ideas" and "matters of fact", a precursor of the analytic/synthetic distinction,
as well as that between those two and on the one hand judgements of value, and on the other the speculations of metaphysics,
had a central place in his philosophy.
His scepticism lead him to consider only the truths of logic and mathematics as known with certainty, and his negative views
about the status of causality and the justification of causal or inductive inference (inter alia) presented to him a problem
in need of resolution.
His resolution of this problem we may find unsatisfactory, for it consisted in showing not why these kinds of inference are
justified notwithstanding that they fail to be logically sound, but in explaining why we will continue to make them irrespective
of their logical status.
This resolution, unsatisfactory though we may find it, is an element consistent with his general conception of philosophical
method, which was inspired by the work of Newton and modelled on the methods of empirical science.
It is for this reason that Hume's major work is entitled "A Treatise on Human Nature", he conceived of his philosophy as differing
in subject matter rather than in method from the work of Newton.
I guess this is naturalism.
Synthetic epistemology is not naturalistic, but is intended to be a synthesis rooted in an understanding of "human nature".