Step 1: Break this into two separate, independent checks: first the verb form, then the pronoun form, since the sentence actually contains two agreement errors tied to the same singular word "each".
Step 2: Verb check: "Each" is always grammatically singular, even when followed by "of the players" (a plural-looking phrase), so the verb must be "was", not "were". This rules out option (b), "was given their kit", partway, and rules out the unedited "were given" pattern.
Step 3: Pronoun check: because "each" is singular, any pronoun referring back to it must also be singular, "his or her", rather than the plural "their". Option (b) fixes the verb ("was") but leaves the plural pronoun "their" uncorrected, so it only solves half the problem.
Step 4: Option (c), "were given his kit", makes the opposite mistake, fixing the pronoun to singular "his" while leaving the verb as plural "were". Option (d), "No improvement", is wrong since the original sentence has two clear errors.
Step 5: Option (a), "was given his or her kit", is the only option that resolves both the verb and the pronoun agreement simultaneously.
Correct option: (1) was given his or her kit.