The translation presents several related problems which affect the verse as a whole.
(a) The second through is implied. As in 9.11-12 (see comments there on through), there is probably a transition from the meaning of movement through (the curtain) to the instrumental meaning “by means of” (his own body). The two phrases will almost certainly need to be translated differently, if this difference of meaning is to be made clear.
(b) If the second through does not mean “by means of,” it must continue the metaphor of movement through the curtain. Two constructions are possible:
(i) “… that is, (through the curtain of) his flesh,” Die Bibel im heutigen Deutsch.
(ii) “that is, (the way of) his flesh.”

(ii) is grammatically more difficult than (i).

The Good News Translation rendering through the curtain—that is, through his own body is both obscure and somewhat misleading, since it tends to equate the curtain with his own body. It is symbolically strange to equate the body which was offered as a sacrifice, with the curtain which divided the outer sanctuary from the inner sanctuary. Though it is true that in English through has two different meanings, the first involving movement and the second involving means, this is certainly not clear to the average reader. Therefore, through the curtain—that is, through his own body may be better expressed as “passing through the curtain, that means, he did this by offering himself as a sacrifice.”
(c) Is the curtain thought of as a “barrier” (compare 9.8; also Mark 15.38) or as a “means of access” (equivalent to way)? The translation of “by means of the curtain” is possible, but less likely than the literal through the curtain, which would make the curtain a “barrier” through which Christ had passed.

The Greek word for opened is the word which was translated went into effect in 9.18, where there was a suggestion of “inaugurating” the covenant by some ceremony. Here the object of opened is way, not “covenant,” and the idea of ceremony is not important. New implies “which did not exist before Jesus opened it” (see 6.20, where Jesus enters before us).

The term way may be both obscure and misleading unless some goal is specified. He opened for us a new way does not refer directly to a new “way of life.” The implication is rather that Christ opened for the believer a new kind of access to God. Therefore He opened for us a new way may be rendered as “He opened for us a new way to God.”

A living way may be unnatural in some languages; how can a way be “alive”? The meaning may be “we can enter the Most Holy Place with perfect freedom by means of Jesus, who sacrificed himself in death but is now alive.” In other words, the living way is Jesus, more particularly Jesus reigning (verses 12-13) and “appearing on our behalf in the presence of God” (9.24). This meaning of a living way may be expressed as “Jesus is that way and he is alive.” Alternatively, living may be understood as “a way which leads to life”; Die Bibel im heutigen Deutsch has “a new way to life,” just as in 9.14 Die Bibel im heutigen Deutsch translated “the living God” as “God, the giver of life” (compare verse 31 and comments).

His own body: Traduction œcuménique de la Bible‘s “his humanity” is misleading; it was not till long after New Testament times that the theology of Christ’s human and divine natures was developed in any systematic way. Body does not refer to his human nature but, like “blood” in verse 19 (Revised Standard Version), to Christ’s whole offering of himself in death.

Quoted with permission from Ellingworth, Paul and Nida, Eugene A. A Handbook on The Letter of the Hebrews. (UBS Handbook Series). New York: UBS, 1983. For this and other handbooks for translators see here .