To determine which compounds obey Huckel's rule, we need to check if they are aromatic.$\\$A compound is aromatic if it is cyclic, planar, fully conjugated, and has $(4n+2)$ $\pi$ electrons, where $n$ is a non-negative integer.$\\$Let's analyze each compound:$\\$• Compound (i): Naphthalene$\\$ - It is cyclic, planar, and fully conjugated.$\\$ - It has 10 $\pi$ electrons.$\\$ - $10 = 4n + 2 \Rightarrow n = 2 \\$ - Obeys Huckel's rule.$\\$• Compound (ii): Cyclopentadienyl anion$\\$ - It is cyclic, planar, and fully conjugated.$\\$ - It has 6 $\pi$ electrons (4 from double bonds + 2 from the anion).$\\$ - $6 = 4n + 2 \Rightarrow n = 1 \\$ - Obeys Huckel's rule.$\\$• Compound (iii): Cyclobutadiene$\\$ - It is cyclic and planar, but not aromatic.$\\$ - It has 4 $\pi$ electrons.$\\$ - $4 \neq 4n + 2 \\$ - Does not obey Huckel's rule.$\\$• Compound (iv): Cyclopropenyl cation$\\$ - It is cyclic, planar, and fully conjugated.$\\$ - It has 2 $\pi$ electrons.$\\$ - $2 = 4n + 2 \Rightarrow n = 0 \\$ - Obeys Huckel's rule.$\\$• Compound (v): Cyclopropenyl anion$\\$ - It is cyclic and planar, but not aromatic.$\\$ - It has 4 $\pi$ electrons.$\\$ - $4 \neq 4n + 2 \\$ - Does not obey Huckel's rule.$\\$• Compound (vi): Cyclooctatetraene$\\$ - It is cyclic and has 8 $\pi$ electrons, but it is non-planar.$\\$ - Does not obey Huckel's rule.$\\$• Compound (vii): Anthracene$\\$ - It is cyclic, planar, and fully conjugated.$\\$ - It has 14 $\pi$ electrons.$\\$ - $14 = 4n + 2 \Rightarrow n = 3 \\$ - Obeys Huckel's rule.$\\$Therefore, the compounds that obey Huckel's rule are:$\\$(i), (ii), (iv), and (vii).$\\$The number of compounds that obey Huckel's rule is 4.$\\$This corresponds to Option 1.