Choice C is correct. The value of $f left parenthesis 2 right parenthesis$ can be found by substituting $2$ for $x$ in the given equation $f (x) = x + 7$ , which yields $f (2) = 2 + 7$ , or $f left parenthesis 2 right parenthesis equals 9$ . The value of $g left parenthesis 2 right parenthesis$ can be found by substituting $2$ for $x$ in the given equation $g left parenthesis x right parenthesis equals 7 x$ , which yields $g left parenthesis 2 right parenthesis equals 7 left parenthesis 2 right parenthesis$ , or $g left parenthesis 2 right parenthesis equals 14$ . The value of the expression $4 f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis$ can be found by substituting the corresponding values into the expression, which gives $4 left parenthesis 9 right parenthesis minus 14$ . This expression is equivalent to $36 minus 14$ , or $22$ .

Choice A is incorrect. This is the value of $f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis$ , not $4 f left parenthesis 2 right parenthesis minus g left parenthesis 2 right parenthesis$ .

Choice B is incorrect and may result from calculating $4 f left parenthesis 2 right parenthesis$ as $4 left parenthesis 2 right parenthesis plus 7$ , rather than
$4 left parenthesis 2 plus 7 right parenthesis$ .

Choice D is incorrect and may result from conceptual or calculation errors.