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Let's say I have a 64 kB Cache provided (i,e 2^18) which is direct mapped and block size is 16 byte = 2^5

Now, in the solution it says m=size of cache in blocks = 4096 = 2^12. This hasn't been provided in the question. So, how do we assume / derive size of cache in blocks was 2^12.

If this is a static value, then does that changes if block size is increased to 32 bytes?

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The size of the cache in blocks is just the size of the cache in bytes divided by the size of a block in bytes. However, both the figures you give are wrong: 64 kB is 2^16 bytes, and 16 bytes is 2^4 bytes. Dividing we get 2^12.

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