It is impossible to renew them again (αδυνατον παλιν ανακαινιζειν). The αδυνατον (impossible) comes first in verse Hebrews 6:4 without εστιν (is) and there is no "them" in the Greek. There are three other instances of αδυνατον in Hebrews (Hebrews 6:18; Hebrews 10:4; Hebrews 11:6). The present active infinitive of ανακαινιζω (late verb, ανα, καινος, here only in the N.T., but ανακαινοω, 2. Corinthians 4:16; Colossians 3:10) with αδυνατον bluntly denies the possibility of renewal for apostates from Christ (cf. Hebrews 3:12-4). It is a terrible picture and cannot be toned down. The one ray of light comes in verses Hebrews 6:8-12, not here.

Seeing they crucify to themselves afresh (αναστραυρουντας εαυτοις). Present active participle (accusative plural agreeing with τους ... παραπεσοντας) of ανασταυροω, the usual verb for crucify in the old Greek so that ανα- here does not mean "again" or "afresh," but "up," sursum, not rursum (Vulgate). This is the reason why renewal for such apostates is impossible. They crucify Christ.

And put him to an open shame (κα παραδειγματιζοντας). Present active participle of παραδειγματιζω, late verb from παραδειγμα (example), to make an example of, and in bad sense to expose to disgrace. Simplex verb δειγματισα in this sense in Matthew 1:19.