Just as you cannot compare two random species today to accurately assess their taxonomy (otherwise we would conclude all crabs form a single family when they actually form at least five distinct groups within the Decapods), we cannot simply compare two random modern languages to decide if they're related.
Instead we need to iteratively work backwards, building up our evolutionary tree, by first comparing the most similar languages and only later looking comparing more distant languages using our knowledge of the modern languages' histories.
Luckily both Indo-European and Semitic are well studied and firmly established families so we have access to information about those older stages.
- Hebrew שש šeš < PS *šidṯ-um (cf Arabic سِتّ sitt, Aramaic שת šeṯ, and in the masculine with the chiastic-concord -at suffix, Akkadian 𒐋 šedištum and Ge'ez ስድስቱ sədstu both showing the original d)
- Russian шесть šestʹ < PIE *s(w)éḱs, with the -t' being a Slavic innovation. The w is in brackets because not all branches show evidence of it, it has been suggested that the original number was in fact *wéḱs, with the initial *s of the following number contaminating it, either replacing the w as in Albanian, Balto-Slavic, Germanic, Indic (& Nuristani), and Italic, or appearing before it as in Celtic, Iranic, and Tocharian. Greek could reflect either an initial *w or *sw, and Armenian likely reflects a form beginning *suw. Other arguments in favour of a lack of an initial *s are the metathesised loan *eks₁w- in Proto-Kartvelian
- Hebrew יש yeš < a form ending in ṯ (cf Aramaic אית ʾīṯ). Note also that the Hebrew is not a verb, but a particle instead
- Russian есть yestʹ < PIE *h₁és-ti (note that the -ti here is inflectional, and not part of the root)
- Hebrew זה ze < a form beginning in ḏ (cf Aramaic די dī & Arabic ذُو ḏū)
- Russian сей/сё sej/sjo (not sure where se came from) < PIE *ḱis
- Hebrew ש־ še < likely from a form with ṯ as it is probably related to its synonym אשר ašer (cf Aramaic אתרא ʾaṯrā, Arabic أَثَر ʾaṯar).
- Russian что što < an extended form of PIE *kʷid. Note that unlike the Hebrew this is also used as an interrogative, which was its original sense.
In many of these cases we see the Hebrew ש š or ז z coming from an earlier dental fricative ṯ or ḏ, where the Russian ш š or с s comes from a dorsal stop ḱ or kʷ. The correspondence sets needed would be:
- Six: Semitic *dṯ ~ PIE *ḱs
- Is: Semitic *ṯ ~ PIE *s
- This: Semitic *ḏ ~ PIE *ḱ
- That: Semitic *ṯ ~ PIE *kʷ
Correspondences between coronal and dorsal stops, when both languages have plenty of both classes are simply not plausible, and the fact we also have inconsistencies in voicing makes it even worse.
Regardless, in all cases we see the forms diverging as we go further back in time rather than converging. This is exactly the behaviour we would expect to see of coincidences, and the opposite of the behaviour we expect to see of genuine connections where the similarity becomes more apparent as we move backwards in time (up the linguistic family tree) and forms converge on the original common ancestor.
Even if these correspondences were plausible though, and we ignore the fact that the similarity disappears as we compare older forms, four apparently similar words is nowhere near enough to establish or even suggest a direct relationship.