Even though the man Adam in the Garden of Eden was not guilty of Eve’s particular method of sin, then just how did Adam transgress?

This question is a normal ‘wondering’ after having understood that Eve didn’t eat an apple in God’s Garden.
Any answer to this on Adam’s actual part in the sin, is just speculation. So with that, we might look at the word ‘touch’ which Eve added to God’s command, as given in Gen.3:3. That word ‘touch’ in the Hebrew is ‘naga’, meaning ‘to lay the hand upon; (euphemism, to lie with a woman)’ (Strong’s no.5060). That particular ‘euphemism’ is a nicer way to say, ‘they had sex’. This might show that Eve was given a ‘particular’ command by GOD concerning her relation to that ‘tree of knowledge of good and evil’, i.e. Satan. The word ‘touch’ (naga) is not associated with Adam’s part in the sin, but with Eve’s. Note also:

1 Tim 2:13-14
13   For Adam was first formed, then Eve.
14   And Adam was not deceived, but the woman being deceived was in the transgression. (KJV)

     According to the Hebrew Manuscripts, Eve was in the ‘particular’ transgression, being of a sexual nature producing the offspring Cain. To say that Adam also had sex with the ‘nachash’ (the serpent, i.e. Satan) would be supposition, with no Scripture support. But we know that Adam did sin along with Eve, as he did eat of what she gave to him, as written in Gen.3:6, and is another euphemism.
I must refrain from Adam’s part as being likewise sexual, based on 1 Tim.2:14, even though they both wore fig leaves on their privates. As an opinion, I myself choose to believe that Adam’s part in the sin was ‘allowing’ Eve to partake, instead of rebuking her to follow God’s Commandment. That would be sin enough during his day.
In military bootcamp, the whole squad is punished at times when just one individual messes up. It is done to work cohesiveness within the group. Individualism doesn’t work too well on the battlefield. Thus, many times we are held responsible for allowing others to commit evils, such as the parent and their young offspring who commits a crime. That’s how I see Adam’s part in the sin, as 1 Tim.2:14 shows Adam was not ‘in the transgression’, meaning his sin was associated with Eve’s act, but different.
See also Rom. 5, as death reigned from Adam to Moses, even though others did not sin ‘after the similitude of Adam’s transgression’. That means ‘others’, such as the sixth day races, and even those born after Adam, have different sins. The main Message is that since flesh came into existence, sin has been, and will always be part of the ‘flesh nature’. The ‘flesh’ of man is not part of God’s original Plan, nor will it be in His Eternity (I Cor.15). Flesh=sin=Death. All three of those will go into the lake of fire, gone forever. So that God could show us that He Only is without sin, He brought His Son in the flesh to conquer Death for us (devil; see Heb.2:14). So if Adam and Eve didn’t begin the first sin and transgression of The Law, a state imparted to all mankind born flesh, then Christ’s Perfect Way He showed us while He was here in the flesh, would not have defeated Satan (devil). And sin is still with us today, and will be until flesh is done away with.
So we could say that God allowed the right conditions to be setup in His Garden, knowing the weakness of the flesh (sin), all in order to begin His Plan for this flesh age. That there was an evil seed spawned of Lucifer is important knowledge for understanding God’s Plan. If it hadn’t happened in such a way, I’m sure our Father would have allowed the sin in another manner. That first sin was necessary for His overall Plan, to show us that we need Him through His Son Jesus Christ.
The ‘fig leaves’ have other links throughout God’s Word, as they refer to the ‘parable of the fig tree’ our Lord gave in Matt.24 and Mark 13. The ‘bad figs’ or ‘evil figs’ of Jer.24, link back to Satan’s ‘thy seed’ of Gen.3:15.