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When simplifying expressions, it's vital to follow the order of operations correctly. The order of operations is a set of rules that ensures consistent results when performing arithmetic on numbers. The most common acronym used is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This way, everyone performs calculations consistently and correctly.

In the given exercise, the operation inside the parentheses, even though it's only a sign in this case, must be considered first. This clears the way for the correct application of multiplication and addition knowing each step is correctly executed. Always check the entire expression and determine the sequence of operations to avoid mistakes.

Multiplication is a fundamental arithmetic operation and often involves multiple rules, especially with negative numbers.

Here, the expression is $$ 14-2(-6)+7$$. Initially, focus on the operation involving multiplication. Notice we have $$-2$$ being multiplied by $$-6$$. Multiplying two negative numbers results in a positive product. So, $$ -2 \times -6 = 12$$.

After this step, the expression transforms into $$14 + 12 + 7$$. This simplifies the problem significantly for the remaining operations.

Remember, whenever you multiply or divide negative numbers, keep track of the signs. The product of two negatives is positive, while the product of a positive and a negative is negative.

Finally, we arrive at addition. After addressing the parentheses and multiplication, we have a simpler expression left to solve, which is $$14 + 12 + 7$$.

Adding numbers together is one of the most straightforward arithmetic tasks. Here, add the numbers step by step. First, $$ 14 + 12 = 26 $$. Then add this result to $$ 7 $$, giving $$ 26 + 7 = 33$$.

Working with addition is often easier towards the end because all complex operations have usually been taken care of. Always double-check your sums in each step to ensure accuracy.

With these strategies, you’ll be able to simplify expressions effectively. Each methodical step builds on the previous to simplify, solve, and verify the final answer.