They are asking for the average memory access time.
If nothing is mentioned whether it is a simultaneous memory access or hierarchical memory access, we need to consider it as hierarchical memory access only. Here in this question nothing is given about read operation so we need to take it as hierarchical memory access for read operation. But for write it is given as write through policy, which will result in simultaneous memory access. Also for write operations write-through cache always go to the main memory, in main memory its hit rate is 100%. Hence Hit rate for write= 1.
Since there are 80% read operations and 20% write operations,
Average memory access time = 0.8 * Time spent for read + 0.2 * Time spent for write
Time spent for read = Hit-rate-for-read * cache access time + Miss-rate-for-read(cache access time + main memory access time)
= ( 0.9 ⨯ 50 + 0.1 ⨯ (500+50) )
= 45+55 = 100
Time spend for write = 500ns (simultaneous write mentioned in question)
Average memory access time = 0.8 * 100 + 0.2 * 500 = 80+100 = 180ns