Arithmetic in different bases

Solution:
Base-6 has 6 digits: 0,1,2,3,4,5. So 4+3 in base 6 is 11. So when we get to the 5+1 in the middle column we note that in bas 6 the sum is 10 which gives another carry.

For the second problem its handy to have a 5's multiplication table - for example in base 5: 3x4=22, 3x2=11, 2x4=13. Then we can add appropriately.