can someone explain this

This one is a little tricky......!!!!   We just have to think about what is going on.......we're just looking for some number > 256^1/4 

So we have

log₂₅₆ b > 1/4      multiply both sides by 4

4log₂₅₆ b > 1       and we can write

log₂₅₆ b⁴ > 1

This says that

b⁴ > 256¹

b⁴ > 256    take the (positive) 4th root of both sides

b > 4