Isiah, absolute value is the distance from zero. Since we measure distance using positive numbers (even if you walk 2 feet backward, you travelled 2 feet), it's why, for example 2 and -2 have an absolute value of 2.
g(-3) = |2(-3) + 1| = |-6 + 1| = |-5| = 5
Since both 5 and -5 are 5 away from zero, they both have an absolute value of 5.
The rest are on you. Go!