While on vacation, erika bought 6 postcards, which was twice as many postcards as nathan bought. samantha bought 4 times as many postcards as nathan. how many postcards did samantha buy?

The answer is 12, I believe.

Write a system of equation based on the problem
⇒ Erika bought 6 postcards
    E = 6
⇒ Erika bought twice as many postcards as Nathan bought
    E = 2N
    2N = E
⇒ Samantha bought 4 times as many postcards as Nathan
    S = 4N

Before we find the number of Samantha's postcards, we need to find the number of Nathan's postcard. Substitute E with 6 in the second equation.
2N = E
2N = 6
  N = 6/2
  N = 3
Nathan bought 3 postcards

Find the number of Samantha's postcard
Substitute N with the number of Nathan's postcards, which is 3, in the third equation
S = 4N
S = 4 × 3
S = 12
Samantha bought 12 postcards