**Explanation:**

To determine the size of the memory system, we need to consider the number of memory chips, the number of address lines, and the number of data lines.

Given:
- Number of memory chips = 8
- Number of address lines = 12
- Number of data lines = 4

**Address Lines:**
The number of address lines determines the number of unique memory locations that can be accessed. Each address line represents a binary digit, so with 12 address lines, we can have 2^12 = 4096 unique memory locations.

**Data Lines:**
The number of data lines determines the number of bits that can be stored or retrieved simultaneously. With 4 data lines, we can store or retrieve 4 bits at a time.

**Memory Chip:**
Each memory chip has a certain storage capacity, which is determined by the number of addressable locations and the number of bits per location.

In this case, each memory chip has 4096 addressable locations (from the 12 address lines) and can store or retrieve 4 bits per location (from the 4 data lines).

**Total Memory System:**
To determine the total storage capacity of the memory system, we need to multiply the capacity of each memory chip by the number of chips.

Capacity of each chip = 4096 locations * 4 bits/location = 16384 bits

Total capacity of the memory system = Capacity of each chip * Number of chips
= 16384 bits * 8 chips
= 131072 bits

To convert the capacity from bits to bytes, we divide by 8 (since there are 8 bits in a byte).

Total capacity of the memory system = 131072 bits / 8 = 16384 bytes

Finally, to convert the capacity from bytes to kilobytes, we divide by 1024 (since there are 1024 bytes in a kilobyte).

Total capacity of the memory system = 16384 bytes / 1024 = 16 kilobytes

Therefore, the size of the memory system is 16 kbytes, which corresponds to option 'A'.

Total size is equal to 2 raise to (adress lines) multiplied with data lines so the correct answer is equal to 2^(12) x 4 = 2^14=2^10 x 2^4 =16 Kb