In a way that leaves no doubt at all. This is the adverb of unequivocal, so it does the same work but attaches to a verb — it tells you HOW something was said, stated, rejected, supported or proved. 'She unequivocally denied it' means the denial had no soft edges, no 'as far as I know', no room to walk it back later. Watch where it likes to sit: right before the verb ('he unequivocally rejected the offer'), or after 'state', 'say' and 'condemn' ('the government condemned the attack unequivocally'). It is a heavy, formal adverb, and it is at its most useful when doubt or hedging was the alternative — which is why you find it clustered around denials, apologies, condemnations, endorsements and scientific conclusions. There is one thing to listen for. Because it is such a strong word, people sometimes use it to make a weak claim sound solid, or to insist rather than to prove: 'I unequivocally reject that accusation.' A native listener often hears a small defensive note there. Said about evidence, it is a statement of fact; said about one's own feelings, it can be a way of raising the volume.