The first series diverges because each successive term is getting multiplied by -3, so the common ratio is larger than 1 in magnitude.
Assuming the second series is
3 - 3/2 + 3/4 - 3/8 + ...
then it converges because the common ratio between terms is -1/2, which is less than 1 in magnitude.
To find the value of the sum, let S denote the n-th partial sum, i.e. the sum of the first n terms in the series:
S = 3 - 3/2 + 3/4 - 3/8 + ... + 3(-1/2)^(n - 2) + 3(-1/2)^(n - 1)
Multiply both sides by -1/2:
(-1/2) S = -3/2 + 3/4 - 3/8 + 3/16 - ... + 3(-1/2)^(n - 1) + 3(-1/2)^n
When we subtract S and (-1/2) S, we see all the middle terms canceling, and we can solve for S:
S - (-1/2) S = 3 - 3(-1/2)^n
S/2 = 3[1 - (-1/2)^n]
S = 6[1 - (-1/2)^n]
As n gets larger, the (-1/2)^n term will converge to 0, leaving us with
lim (n -> infinity) S = 6
so that the series converges to 6.