Suppose a population of 250 crickets doubles in size every 6 months. How many crickets will there be after 2 years?

There are 12 months in a year, so 2 years is equal to 2 x 12 = <<2*12=24>>24 months.

If the population doubles every 6 months, then in 24 months, the population will double 24/6 = <<24/6=4>>4 times.
So, the total number of crickets after 2 years will be 250 x 2^4 = 250 x 16 = <<250*16=4000>>4000 crickets. Answer: \boxed{4000}.