1. “A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.”

But according to my book, 6(3) means “6 times 3”.
So,
16/4(4) = ? is the same with 16/4*4 = ?
because
4(4) means “4 times 4”
and
4*4 means “4 times 4”

It was not stated if P in PEMDAS stands for P as a sign of grouping or P as a sign of multiplication.

Sources:

College Algebra by William Hart 4th edition, page 5

2. Originally Posted by Marvin Kalngan

“A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.”

But according to my book, 6(3) means “6 times 3”.
So,
16/4(4) = ? is the same with 16/4*4 = ?
because
4(4) means “4 times 4”
and
4*4 means “4 times 4”

It was not stated if P in PEMDAS stands for P as a sign of grouping or P as a sign of multiplication.

Sources:

College Algebra by William Hart 4th edition, page 5
Hi Marvin!

That is correct.
6(3) is shorthand for $6 \times (3)$.

So:
$16/4(4) = 16 / 4 \times (4) = 4 \times 4 = 16$

And P in PEMDAS stands for Parentheses, which groups an expression.
The operation applied to it can be anything.
If no operation is specified, than multiplication is intended.