Multiply matrix B by matrix C where B = [-2 6] and C = [3; 4].

The matrices are given as:

Matrix B has 1 row and 2 columns, so its dimension is $1 \times 2$.
Matrix C has 2 rows and 1 column, so its dimension is $2 \times 1$.

For matrix multiplication BC to be defined, the number of columns in B must be equal to the number of rows in C.
Number of columns in B = 2.
Number of rows in C = 2.
Since $2 = 2$, the multiplication is possible, and the resulting matrix BC will have dimensions $1 \times 1$.

To find the product BC, we multiply the elements of the row of B by the corresponding elements of the column of C and sum them.

The final answer is $\begin{pmatrix} 18 \end{pmatrix}$.