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So, you ask about what is the leading coefficient? You can just simply say that the leading coefficient is the numerical coefficient of the  leading term. How to find the leading term?
Question: What is the leading term?
Let's analyze first the terms. The terms are:
To find the leading term, you base it on the term that has the highest degree, to find the degree, you base it on the exponent or you can also say, the number of variables in that term.
3x=(1 variable=x) degree=1
-x^2=[2 variables= x and x(there are two x's because it was x squared]degree=2
8=(it is a constant, there are no variables obviously, so the degree is 0)degree=0
Now we can conclude that the term -x^2 has the highest degree followed by the terms 3x an 8 respectively. Since x^2 has the highest degree, it is the leading term and should go first. So, it is arranged in ascending degrees like this.
Now, WHAT IS THE LEADING COEFFICIENT!!  Answer: The numerical coefficient of the leading term. 
The leading term=-x^2
Numerical Coefficient=-1
How about the leading coefficient of 5x^3+6x+4
Answer: 5