u = ⟨-2, 6⟩
v = ⟨3, 2⟩
w = ⟨-1, 4⟩
u + v = ⟨-2, 6⟩ + ⟨3, 2⟩
u + v = ⟨-2 + 3, 6 + 2⟩
u + v = ⟨1, 8⟩
2 (u + v) = 2 ⟨-1, 8⟩
2 (u + v) = ⟨2 • 1, 2 • 8⟩
2 (u + v) = ⟨2, 16⟩
-3 w = -3 ⟨-1, 4⟩
-3 w = ⟨-3 • (-1), -3 • 4⟩
-3 w = ⟨3, -12⟩
2 (u + v) - 3 w = 2 (u + v) + (-3 w)
2 (u + v) - 3 w = ⟨2, 16⟩ + ⟨3, -12⟩
2 (u + v) - 3 w = ⟨2 + 3, 16 + (-12)⟩
2 (u + v) - 3 w = ⟨5, 4⟩
Then the magnitude of this vector is
||2 (u + v) - 3 w|| = √(5² + 4²) = √41 ≈ 6.403
so the second choice is correct.