John 8:4

λέγουσιν αὐτῷ, πειράζοντες, Διδάσκαλε, αὕτη ἡ γυνὴ κατελήφθη ἐπ᾽ αὐτοφόρῳ μοιχευομένη.

RBT Greek Interlinear:

Strongs 3004; legousin; λέγουσιν; say; V-PIA-3P

Strongs 846; autō; αὐτῷ; to himself; PPro-DM3S

Strongs 1320; Didaskale; Διδάσκαλε; Teacher; N-VMS

Strongs 3778; hautē; αὕτη; she; DPro-NFS

Strongs 3588; hē; ἡ; the; Art-NFS

Strongs 1135; gynē; γυνὴ; woman; N-NFS

Strongs 2638; kateilēptai; κατείληπται*; was caught; V-RIM/P-3S

Strongs 1909; ep’; ἐπ’*; upon; Prep

Strongs 1888; autophōrō; αυτοφώρῳ*; self-observation; Adj-DNS

Strongs 3431; moicheuomenē; μοιχευομένη; she who is committing adultery; V-PPM/P-NFS

RBT Hebrew Literal:

αὐτο-φώρᾱτος - self betrayed/self Exposed

They are saying to himself, "Teacher, herself, the Woman, was overtaken upon self-betrayal, she who commits adultery.^80a

Julia Smith Literal 1876 Translation:
They say to him, Teacher, this woman was taken committing adultery, in the very act.

LITV Translation:
they said to Him, Teacher, this woman was taken in the very act, committing adultery.

ESV Translation:
they said to him, “Teacher, this woman has been caught in the act of adultery.

Footnotes

80a

The word "ἐπαυτοφώρῳ" (epautophōrō) occurs only once here in the NT. Generally when a special word shows up in the NT there is a really good reason for it. 

1. "ἐπί" (epi): A preposition meaning "upon" or "in."

2. "αὐτόφωρος" (autopōros): An adjective derived from "αὐτό" (auto), meaning "self," and "φωρός" (phōros), meaning "watching" or "observation." "ἐπαυτοφώρῳ" (epautophōrō) functions as an adverbial form of "αὐτόφωρος" (autopōros).

So, "ἐπαυτοφώρῳ" (epautophōrō) means "upon oneself being caught" or "caught in the act by oneself," indicating that the action described happened while the subject was directly observed or caught in the act.

The literal translations of "ἐπαυτοφώρῳ" (epautophōrō) are:

1. Upon self-observation.
2. Caught by oneself.
3. Self-caught.
4. Caught in the act by oneself.
5. Caught red-handed by oneself.