Answer:
truth.
Explanation:
The word "avouch" is an old-fashioned word, which means "truth".
In Act 1, Scene 1, two Bernardo, an officer and Marcellus, a watchmen, asks Horatio, a friend of Prince Hamlet, to stand guard with them that night because they have seen the apparition and they want to show him too. But Horatio, do not belie them until he sees that apparition with his very own eyes. In the excerpt the ghost that appears to all three men was the apparition of the deceased King of Denmark.
When, Horatio saw the ghost with his own eyes he believed that it is the ghost of the deceased king. And states:
"Before my God, I might not this believe
Without the sensible and true avouch
Of mine own eyes."
meaning, Horatio would not have believed this (swearing to God), if he truly and sensibly (in his senses) had seen the ghost with his own eyes.
