To subtract the polynomial \(4x^2 - 3x + 5\) from \(6x^2 + x - 2\), we can express this operation as:
\[ (6x^2 + x - 2) - (4x^2 - 3x + 5) \]
Now, distribute the negative sign across the second polynomial:
\[ 6x^2 + x - 2 - 4x^2 + 3x - 5 \]
Next, combine like terms:
- For the \(x^2\) terms: \(6x^2 - 4x^2 = 2x^2\)
- For the \(x\) terms: \(x + 3x = 4x\)
- For the constant terms: \(-2 - 5 = -7\)
Putting it all together, we have:
\[ 2x^2 + 4x - 7 \]
So, the result of the subtraction is:
\[ \boxed{2x^2 + 4x - 7} \]
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