Your question is far more a question about translation theory than text criticism. The text in that verse is stable. In fact, there seem to be no variations in the Greek manuscripts handed down to us. “φωτισθέντας” (Ἑβραίους 6·4 THGNT-T) ("enlightened") is the word.
As you asked, how then could the Peshitta have ”ܠܡܰܥܡܽܘܕܺܝܬܳܐ“ (Hebrews 6:4 PESHNT-T)? The Peshitta is, what today we would call a "mediating" translation. It lies in the middle between formal (dragging the source language, sometimes kicking and screaming, into the target text)and functional (carrying over the meaning from the source to the target language even if it means picking new words in the target text). Here is an example of them taking a functional approach, carrying over the idea, rather than the Greek word.
How could this be? Let's ask a different question: When is it that a person is enlightened? Up until relatively recent times, baptism was understood as the tool that God uses to create faith and convey forgiveness to a person. So the translators of the Peshitta are taking what is implicit and making it explicit.
And just in case there might be some people who might challenge the notion that, to the early church (and for many, many centuries after), baptism brings enlightenment, here are some quotes from the church fathers to illustrate the context:
THEODORET OF CYR: It is out of the question, he is saying, for those
who have approached all-holy baptism, shared in the grace of the
divine Spirit and received the type of the eternal goods to make their
approach again and be granted another baptism.
<Erik M. Heen and Philip D. W. Krey, eds. Hebrews. vol. 10 of Ancient
Christian Commentary on Scripture. ICCS/Accordance electronic ed.
(Downers Grove: InterVarsity Press, 2005), 84.>
EPHREM THE SYRIAN: “It is impossible to restore again to repentance”
through a second baptism “those who have once been baptized, who have
tasted the heavenly gift” through the medicine which they received,
“have become partakers of the Holy Spirit” through the gifts received
from the Spirit, “have tasted the goodness of the Word of God” in the
new gospel and were armed with the power of the age to come in the
promises prepared for the pious ones, but now “have fallen away”
again. Those who propose two baptisms ask for the crucifixion again of
the Son of God and for his dishonor.
<Erik M. Heen and Philip D. W. Krey, eds. Hebrews. vol. 10 of Ancient
Christian Commentary on Scripture. ICCS/Accordance electronic ed.
(Downers Grove: InterVarsity Press, 2005), 84-85.>
SEVERIAN OF GABALA: The apostles raised the dead. And this was the
power of the resurrection. He said, “hold him up to contempt,” because
if baptism is a mystery, it suffices once and for all. And if the
matter happens a second time, it is an act of despising and ridicule.
FRAGMENTS ON THE EPISTLE TO THE HEBREWS 6.6.
<Erik M. Heen and Philip D. W. Krey, eds. Hebrews. vol. 10 of Ancient
Christian Commentary on Scripture. ICCS/Accordance electronic ed.
(Downers Grove: InterVarsity Press, 2005), 85.>
AMBROSE: ... So, then, that which he says in this epistle to the
Hebrews, that it is impossible for those who have fallen to be
“renewed unto repentance, crucifying again the Son of God and putting
him to open shame,” must be considered as having reference to baptism,
wherein we crucify the Son of God in ourselves that the world may be
by him crucified for us. We triumph, as it were, when we take to
ourselves the likeness of his death. We put to open shame upon his
cross principalities and powers and triumphed over them, that in the
likeness of his death we, too, might triumph over the principalities
whose yoke we throw off. But Christ was crucified once and died to sin
once, and so there is but one, not several baptisms. . . .
<Erik M. Heen and Philip D. W. Krey, eds. Hebrews. vol. 10 of Ancient
Christian Commentary on Scripture. ICCS/Accordance electronic ed.
(Downers Grove: InterVarsity Press, 2005), 85-86.>
CHRYSOSTOM: “They crucify,” he says, “the Son of God on their own
account and hold him up to contempt.” What he means is this. Baptism
is a cross, and “our old self was crucified with him,” for we were
“united with him in a death like his” and again, “we were buried
therefore with him by baptism into death.” Therefore, it is not
possible that Christ should be crucified a second time, for that is to
“hold him up to contempt.” For if “death no longer has dominion over
him,” if he rose again, by his resurrection becoming superior to
death, if by death he wrestled with and overcame death, and then is
crucified again, all those things become a fable and a mockery. He
then that baptizes a second time crucifies him again. . . .
<Erik M. Heen and Philip D. W. Krey, eds. Hebrews. vol. 10 of Ancient
Christian Commentary on Scripture. ICCS/Accordance electronic ed.
(Downers Grove: InterVarsity Press, 2005), 87.>