Finally, results of the proposed technique and existing
technique are compared which show that our proposed technique acts significantly to achieve better
results in terms of cost, wait, and time of the appliances.
the words in bold are followed s or not. Kindly guide me.
The title “S and es” implies that you’re treating “show” and “acts” as nouns. These words, however, are capable of being used both as a noun and as a verb, and in your quote the two words are being used as verbs. You can see the question below (actually very recent!) on another example of this:
And yes, these verbs are conjugated correctly. “Show” is third-person plural, which works with “proposed technique and existing technique” as the subject. Meanwhile, “acts” is third-person singular, which works with “proposed technique” as the subject.
(By the way, rewriting “proposed technique and existing technique” to “proposed and existing techniques” makes the tense a lot clearer.)