Understanding the basic concepts in memory organisation
One can derive the page size from knowing that the page table has three levels, the virtual address space is 46 bits (assume byte addressing), and a PTE is 4 bytes. P bits (where P = log2(page_size)) of the virtual address are not involved in the translation (these provide the offset within the page), so the three levels must translate a 46-P bit address value.

Each node of the page table contains page_size/PTE_size entries, and so each node covers log2(page_size/PTE_size) bits, which is P-2 bits. The page size can then be derived since 46 = (P-2)*3 + P.

(In a simple hierarchical page table, the first level is a single page [in the given design providing 2(P-2) entries]. Each valid entry points to a page-sized table at the second level. Likewise each valid entry in the second level points to a page-sized table in the third level. Each valid entry in the third level provides a page translation. If all the first and second level entries were valid, there would be 2(P-2) * 2(P-2) third level tables each with 2(P-2) entries. Thus 2(P-2)*3 entries would be available, each covering 2P (page_size) bytes.)

With respect to page coloring, one must determine the number of bits that are not part of the page offset which are used for indexing the cache. The number of sets is equal to cache_size/block_size/associativity, so to index to a specific set requires log2(cache_size/block_size/associativity) bits. The offset within the block uses log2(block_size) bits. Using C= log2(cache_size), B= log2(block_size), and A=log2(associativity), C-B-A bits are used to index the set and C-B-A+B, i.e. C-A, bits are used to address the given byte.

Since only P bits are provided as part of the page offset, C-A-P bits use virtual address bits. In order to avoid the problem of two different virtual addresses with the same physical address mapping to different sets, the virtual addresses of any physical pages that are so shared can be colored, i.e., share the same value for the C-A-P virtual address bits. (This forces them to map to the same set. With tagging based on physical addresses, this is sufficient to avoid aliasing issues like a write to one virtual address not updating a cached entry at the same physical address but a different virtual address.)

Each index group is called a color, so to provide C-A-P virtual address bits requires 2(C-A-P) colors.

(The above assumes an "ordinary" cache. Indexing not using simple modulo 2N, e.g., skewed associativity, would have different coloring requirements; but such complexities are typically ignored for problems like this.)