The best option to fill in the blank is: should

The sentence would be: "She advised that I should avoid wasting time with the mobile."

Here's why the other options wouldn't fit as well:

• May: This can indicate possibility or permission, but in this context, the advice implies a recommendation or suggestion for action, not merely stating a possibility.
• Can: This highlights ability, but the sentence focuses on what is advisable, not what is technically possible.
• Might: This suggests a weaker level of suggestion compared to "should," making it less appropriate for conveying the emphatic advice of avoiding wasting time.

"Should" expresses a strong recommendation or suggestion for what is considered the right or best course of action. It effectively conveys the intention of the advice without sounding too forceful or intrusive. Therefore, "should" best aligns with the context of the sentence and the speaker's intention.