Welcome, El Ectric
Hobbes is not the easiest historical philosopher to interpret; and the area of your question is still much contested but I think I can provide pointers towards an account that will make some things clearer.
Subjective theory of value
Hobbes is widely regarded as a subjectivist about value on the basis of texts such as the following:
whatsoever is the object of any mans Appetite or Desire; that is it, which he for his part calleth Good: And the object of his Hate, and Aversion, evill. (Leviathan, VI: https://www.gutenberg.org/files/3207/3207-h/3207-h.htm.)
Good, and Evill, are names that signifie our Appetites, and Aversions; which in different tempers, customes, and doctrines of men, are different: And divers men, differ not onely in their Judgement, on the senses of what is pleasant, and unpleasant to the tast[e], smell, hearing, touch, and sight; but also of what is conformable, or disagreeable to Reason, in the actions of common life. Nay, the same man, in divers times, differs from himselfe; and one time praiseth, that is, calleth Good, what another time he dispraiseth, and calleth Evil. (Leviathan, XV: https://www.gutenberg.org/files/3207/3207-h/3207-h.htm.)
‘Subjective’ if we are to apply the term here means something like ‘expressive of emotion or preference’, neither of which connects with truth or knowledge. ‘This is good’ on Hobbes’ account signifies only that I feel in a certain way towards something. ‘This is good’ is not capable, at least in the light of such texts, of truth and it cannot embody knowledge.
Objective theory of action
At this point we need to introduce Hobbes’ ideas about the ‘laws of nature’.
A law of nature is a dictate of reason or more precisely:
A LAW OF NATURE, (Lex Naturalis,) is a Precept, or generall Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life, or taketh away the means of preserving the same; and to omit, that, by which he thinketh it may be best preserved. For though they that speak of this subject, use to confound Jus, and Lex, Right and Law; yet they ought to be distinguished; because RIGHT, consisteth in liberty to do, or to forbeare; Whereas LAW, determineth, and bindeth to one of them: so that Law, and Right, differ as much, as Obligation, and Liberty; which in one and the same matter are inconsistent. (Leviathan, XIV: https://www.gutenberg.org/files/3207/3207-h/3207-h.htm.)
The laws of nature concern such matters as promise-keeping, justice, gratitude; nineteen of them are listed in Leviathan, XIV-XV.
Hobbes’s view is that the laws of nature provide the indispensable framework for civil peace, hence for personal security. This is so regardless of my or anybody else’s emotions or preferences. That’s one non-subjective fact. Another is that personal security – self-preservation – is an inherent and overriding end or goal of the human agent. (Note, we are only representing Hobbes’ standpoint.)
The laws of nature actually ‘bind’ and we have an obligation to adhere to them but there is a complication:
Onely When There Is Security The Lawes of Nature oblige In Foro Interno; that is to say, they bind to a desire they should take place: but In Foro Externo; that is, to the putting them in act, not alwayes. For he that should be modest, and tractable, and performe all he promises, in such time, and place, where no man els should do so, should but make himselfe a prey to others, and procure his own certain ruine, contrary to the ground of all Lawes of Nature, which tend to Natures preservation. And again, he that shall observe the same Lawes towards him, observes them not himselfe, seeketh not Peace, but War; & consequently the destruction of his Nature by Violence. (Leviathan, XVI: https://www.gutenberg.org/files/3207/3207-h/3207-h.htm.)
The point is that it does not pay the individual to adhere to the laws of nature solo, irrespective of whether others also adhere. The laws of nature are the framework for civil peace only if everybody adheres to them. At this point Hobbes introduces the sovereign, who is authorised by everyone to enforce the laws of nature. It is safe for me to obey these laws since the sovereign ensures that no-one can endanger my personal security by breaking the laws while I comply with them. Moreover, ‘to conferre all … power and strength’ on the sovereign in the interests of civil peace and self-preservation’ (Leviathan, XVII: https://www.gutenberg.org/files/3207/3207-h/3207-h.htm) is another dictate of reason since it is the only effective way to ‘seek’ or ‘endeavour’ peace (1st law of nature, XIV).
There is uncertainty about the kind of obligation that attaches to obeying the laws of nature. Is this some kind of ethical obligation, beyond the moral subjectivism outlined at the start, or is it (merely) a rational constraint to create and maintain the essential conditions for our self-preservation?
Stephen Darwall, ‘Normativity and Projection in Hobbes's Leviathan’, The Philosophical Review, Vol. 109, No. 3 (Jul., 2000), pp. 313-347.
Mark C. Murphy, ‘Deviant Uses of "Obligation" in Hobbes' "Leviathan"’, History of Philosophy Quarterly, Vol. 11, No. 3 (Jul., 1994), pp. 281-294.
Tom Sorell, Hobbes, London: Routledge & Kegan Paul, 1986, ch. VIII & IX.
Elijah Weber, ‘Rebels with a Cause: Self-Preservation and Absolute Sovereignty in Hobbes’s “Leviathan”’, History of Philosophy Quarterly, Vol. 29, No. 3 (JULY 2012), pp. 227-246.