The word "equal" has three parts of speech: noun, verb, and adjective.
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four plus two equals six
In your first example sentence, "equal" is being used as a verb in the third person singular form: equals.
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four plus two is equal to six
In your second example, "equal" is being used as an adjective, and so it needs to employ a linking verb (in this case, "be" or "is") before it. The "to" after it is a preposition.
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four plus two is six
Finally, here "is" is again a linking verb in an S + LV + C pattern (Subject + Linking Verb + Complement).
