Final answer:
The line 'Loving offenders thus I will excuse ye' from 'Astrophil and Stella' indicates the speaker is hopelessly in love, as it shows an unconditional willingness to forgive the beloved's faults.
Step-by-step explanation:
The line from Sonnet 8 from Astrophil and Stella by Philip Sidney that indicates the speaker is hopelessly in love is "Loving offenders thus I will excuse ye" (option d). This line suggests that the speaker is willing to forgive the faults of those he loves, indicating a deep sense of infatuation and unconditional love, typical of a lover ensnared by their emotions.
Option a does not pertain to personal love, rather it addresses the origin of love, Greece. Option b exhibits indignation rather than hopeless love, and option c merely presents an image and doesn't effectively convey a sense of being love-struck.