Simplify the Expression: 2a+3b-6(a-2b) Using Distributive Property

To solve this problem, we'll apply the distributive property and combine like terms.

• Step 1: Apply the distributive property.
  We have the expression $2a + 3b - 6(a - 2b)$. Let's distribute the $-6$ across the terms inside the parentheses:
  $-6(a - 2b) = -6 \cdot a + (-6) \cdot (-2b) = -6a + 12b$.
• Step 2: Combine like terms.
  Now substitute $-6a + 12b$ back into the expression:
  $2a + 3b - 6a + 12b$.
  Combine the like terms, $2a$ and $-6a$, and $3b$ and $12b$:
  $(2a - 6a) + (3b + 12b) = -4a + 15b$.

Therefore, the simplified expression is $-4a + 15b$, which matches choice 2.