Let's denote the unknown number by x.

6 is added to twice a number and this sum is multiplied by 5 is represented by the expression:

(6 + 2x)*5

The number is multiplied by -3 and 4 is added to the product is represented by the expression:

x*(-3)+4

The two expressions need to be equal thus the equation that we need to solve is:

(6 + 2x)*5 = x*(-3)+4

........

click here to see the equation solved for x

........

x = -2

Indeed:

(6 + 2*(-2))*5 = (6 + (-4))*5 = 2*5 = 10

(-2)*(-3)+4 = 6+4 = 10

The number is -2.