To solve this problem, we need to understand how X-linked conditions are inherited.$\newline$An X-linked condition is one that is associated with a gene located on the X chromosome.$\newline$Let's analyze the inheritance pattern:$\newline \bullet$A woman has two X chromosomes, one of which carries the X-linked condition.$\newline \bullet$When she has children, she can pass on either of her X chromosomes to her offspring.$\newline \bullet$If she passes the X chromosome with the condition to her son, he will inherit the condition because males have one X and one Y chromosome (XY).$\newline \bullet$If she passes the X chromosome with the condition to her daughter, the daughter will be a carrier if the other X chromosome is normal, or affected if both X chromosomes carry the condition.$\newline$Therefore, the X chromosome with the condition can be inherited by both sons and daughters.$\newline$Thus, the correct answer is Option 4: Both sons and daughters.