First multiply by 10 because 460 ends in zero: 12230. Now we only have to multiply by 46 which we can do by long multiplication:
We can leave off the zero and just do 1223*46:
..1223
...x.46 (46 times 1223)
......18--------6*3 (this part calculates 6*1223)
....120--------6*2
..1200--------6*2
..6000--------6*1
..7338 +
....120--------4*3 (this part calculates 40*1223)
....800--------4*2
..8000--------4*2
40000--------4*1
56258 (we add the previous 5 rows together so we have (40+6)*1223, which is the same as 46*1223).
Now we have to add in that zero that was at the end of 460: 562580 is the final answer.