Assuming that the filter function is the one in the dplyr package and that the asterisks were added just for emphasis in your post, there is no need for the $. The code should be
The $ is used to get a specific column from a data frame. If you wanted to store the values of the market_segment column in a separate vector, you could write
NewVec <- hotel_bookings$market_segment
Within the filter function, you give the name of the data frame as the first argument, as seen in your code, and then the column names can be used as bare names with no quotes and no explicit reference to the data frame in the subsequent arguments of the function.