To solve the expression \(-6 + 3 \times 5 \div \sqrt{16} + 32 \div 8\), we need to follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):
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Calculate the square root and divisions: \[ \sqrt{16} = 4 \] \[ 32 \div 8 = 4 \]
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Now, substitute these values back into the expression: \[ -6 + 3 \times 5 \div 4 + 4 \]
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Next, do the multiplication and division from left to right: \[ 3 \times 5 = 15 \] \[ 15 \div 4 = 3.75 \]
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Now substitute that back into the expression: \[ -6 + 3.75 + 4 \]
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Finally, perform the addition and subtraction from left to right: \[ -6 + 3.75 = -2.25 \] \[ -2.25 + 4 = 1.75 \]
So, the final result is:
\[ \boxed{1.75} \]