Is it possible to define the matrix $A + B$when $A$ has $2$columns and $B$has $4$columns?

Hint: First we have to define what the terms we need to solve the problem are.
First we need to know about the column matrix; which is an element only in one column is known as or called as the column matrix, similarly as per row matrix there is only one row element or variable.

Complete step by step answer:
Let the given question contains the first matrix is $A$ has $2$columns which means elements only in two columns and the $B$has $4$columns which means four columns of elements;
Since A has two columns which means $\left( {\begin{array}{*{20}{c}}
  {{a_{11}}}&{{a_{12}}} \\
  {{a_{21}}}&{{a_{22}}}
\end{array}} \right)$
(here we seen that there are two columns and two rows)
and
 $\left(
  a \\
  b \\
  \right)$
 is also two column matrices as per definition.
So then similarly a four-column matrix is containing four columns must and in rows there is no restriction;
And the addition properties say the sum of the of two or more than two terms equal to the new resultant thus; for summing the two-column matrix and four column matrices does not going to yields
Or it is not able to determine;
Since the number of two column matrix and the number of four column matrix of both rows and columns are same or in different rows too, we only occur in each matrix must be same
And hence we cannot able to sum $A + B$= $\left( {\begin{array}{*{20}{c}}
  {{a_{11}}}&{{a_{12}}} \\
  {{a_{21}}}&{{a_{22}}}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  {{a}}&{{b}}&{c}&{d} \\
  {{d}}&{{c}} &{b}&{a}
\end{array}} \right)$
 is undetermined.

Note: Since generally in the column two matrices have $2 \times 2$(square matrix) and also the general term of matrix of columns with four is$4 \times 4$.
In a matrix the inside elements are called numbers or variables.