The best answer choice is C: "While failing to describe his lover's beauty, he still manages to flatter her." Petrarch's "Sonnet 18" is about Laura's beauty and the way it evades proper description. As such, Petrarch feels he is not equipped to truly praise Laura in the way she deserves to be praised.
In the first couple of lines, Petrarch admits,
Ashamed sometimes thy beauties should remain
As yet unsung, sweet lady, in my rhyme;
Here, Petrarch expresses the idea that it is a shame Laura's beauty should not be immortalized in poetry. He can remember the first time he saw her, as he recounts in lines 3-4, yet he does not feel he can adequately capture her beauty in words. He continues,
But no fit polish can my verse attain,
Not mine is strength to try the task sublime: (5-6)
Petrarch laments that he cannot produce a poem as "sublime" as Laura's beauty. He just feels as though he cannot get it quite right. He does not have the ability or the "strength" to write a poem that can do Laura justice.
These feelings, though, do not stop Petrarch from trying. He concludes the poem by saying,
But ah, the pen, the hand, the vein I boast,
At once were vanquish'd by the mighty theme! (13-14)
The word "vanquished" indicates that in all of his attempts, Petrarch still feels defeated by Laura's beauty. It is stronger than his ability to illustrate her image in his poetry.
Because Petrarch is saying he cannot write a poem to adequately express Laura's beauty, he manages to produce a sonnet that praises her beauty and even by saying how indescribable it is, pays homage to Laura's power over him. Therefore, the best answer is C.
The best option would appear to be C. Petrarch is lamenting how hard it is for his poetry, no matter how skillful it may be, to capture fully the beauty of his muse. Her beauty is so great that to put it into words is beyond the poet's abilities. Although Petrarch is referring to a specific muse—in this case, Laura—he's also making a general point about the inability of poetry, or indeed any art form, to do complete justice to the beauties of this world. Nevertheless, art can certainly hint, suggest, direct our attention to what is beautiful in the world around us. And works of art, including poems, can be beautiful in and of themselves, partaking in that ideal form of beauty partially reflected in beautiful faces, beautiful things.
The correct answer is C. The interpretation of the sonnet is as follows:
Lines 1–2: The poet declares he is ashamed that he has not yet written a poem about the lady's beauty.
Lines 3–8: The poet explains that the reason he has not written a poem about the lady's beauty is that he is not skillful or talented enough to create a poem that would do justice to her beauty, so he has not made the attempt.
Lines 9–14: The poet describes trying to write a poem about the lady's beauty but stopping before completing the work because the theme proved too high to be captured in verse.
The sonnet is obviously ironic. The poet is saying that the lady's beauty is so great that it demands a poem as a tribute, but that because her beauty is so great, no poem can be written that would do it justice. Nevertheless, this poem about not being able to write such a poem becomes the poem he says he has been unable to write. The question asks about insincerity. One might consider his words insincere, but they are better understood as playfully ironic. Either way, choice C is true. The poet never describes the lady's beauty in the poem, but he arguably does more than that by claiming that her beauty is so great that it defies description. Thus he flatters her without describing her beauty.
If those four are your options, I would have to go with C. It is the only one that makes sense.
To me, what the poem is saying is basically "you are so wonderful and beautful that I can't even manage to write a poem about or talk about you -- you're just too good for words."
If that's what he's talking about in this poem, then only C really makes sense. He's not really trying to get attention for himself so it's not A. He never claims his love is a secret so it's not B. He doesn't praise himself in the last lines so it's not D.
C kind of makes sense because he does flatter her even though he can't actually describe her.