Russian voiced consonants are pronounced as their voiceless counterparts when they appear at the end of a word and before a voiceless consonant. Voiced/Voiceless: Б/П В/Ф Г/К Д/Т Ж/Ш З/С For example: год [гоТ] - year завтра [заФтра] - tomorrow So, according to the rule "без" and "через" are pronounced with "c" at the end.

It's common rule of Russian. "з" sounds like "с" in the end of the word. If the word is followed by other word beginning with a vowel or a voice consonant, and there is no pause between them, then "з" keeps its voice. Examples: через день [cherezden'], через час [chereschas], без обмана [bezobmana], без причин [besprichin]. NOTE: беспричинно (adverb), чересполосица (noun).

s before a pause or an unvoiced consonant (к, х - п, ф - т, ч, ц, ш, щ) через реку /черезреку/ через овраг /черезовраг/ через ... реку /черес реку/ через... овраг /череc овраг/ через кусты /черескусты/

That's a difficult question. It depends on what sound comes next. For example in "без образования" it sounds like Z and in "без правил" it sounds like S. I guess we need more experienced linguist to explain all the cases.