Multiplying a 4digit number by a 1 or 2digit number
In a nutshell
Multiplying fourdigit numbers by one and twodigit numbers require short and long multiplication, as they are too long to be worked out mentally.
Written multiplication methods
The long and short multiplication methods are written methods where columns are used to set out multiplication calculations.
Multiplying a fourdigit number by a onedigit number
When multiplying a fourdigit number by a onedigit number, short multiplication is used. The calculation is set out as usual and multiplication by the number happens from right to left in columns.
Example 1
What is $1352\times6$?
Set out the calculation.
$\begin{array}{cccc}&\text{Th} & \text{H} & \text{T} & \text{O} \\& 1& 3 & 5 & 2 \\\times & & && 6 \\ \hline&&&& \\ \hline&&&&\end{array}$
Multiply each digit of the fourdigit number by six.
$2\times6=12\\5\times6=30\\3\times6=18\\1\times6=1$
Place each answer in the correct column, carrying and adding where necessary.
$\begin{array}{cccc}&\text{Th} & \text{H} & \text{T} & \text{O} \\& 1& 3 & 5 & 2 \\\times & & && 6 \\ \hline&8&1&1& 2\\ \hline&^2&^3&^1&\end{array}$
$1352\times6=\underline{8112}$
Multiplying a fourdigit number by a twodigit number
Multiplying by a twodigit number is almost the same  the only difference is that the two digit number has to be partitioned into tens and units. This method is known as long multiplication.
PROCEDURE
1.
 Set out the calculation:  Write your numbers one below the other, in columns where tens and ones line up.
 Draw a multiplication symbol on the left.

2.
 Partition the twodigit number into tens and units and multiply each separately.

3.
 Adjust zeros accordingly. 
4.
 Add the answers together. 
Example 2
What is $1784\times27$?
Set out the calculation.
$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &2& 7 \\ \hline& &&&& \\+& &&&& \\ \hline& &&&& \end{array}$
Partition $27$ into tens and ones.
$27=20+7$
First multiply by the ones.
$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &2& \underline7 \\ \hline& ^11&^52&^54&^28&8 \\+& &&&& \\ \hline& &&&& \end{array}$
Then multiply by the tens.
Treat $20$ as $2$, then add a zero in the first column.
$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& &&&&0 \\ \hline& &&&& \end{array}$
Continue multiplying by $2$.
$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& ^13&^15&6&8&0 \\ \hline& &&&& \end{array}$
Add the results.
$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& ^13&^15&6&8&0 \\ \hline& 4&^18&^11&6&8 \end{array}$