To solve the expression \( 44 - 14 \times 6 \div 28 \), we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
First, perform the multiplication and division from left to right: \[ 14 \times 6 = 84 \] Now the expression is: \[ 44 - 84 \div 28 \]
Next, divide: \[ 84 \div 28 = 3 \] Now the expression is: \[ 44 - 3 \]
Finally, perform the subtraction: \[ 44 - 3 = 41 \]
Thus, the result of the expression is \( \boxed{41} \).