given the following values, what is angle B?

A= 46 degree
b= 4
c= 8

Presumably, a is opposite angle A, etc.

By law of cosines,

a^2 = b^2 + c^2 - 2bc cos A
= 16 + 64 - 2*4*8*0.69
= 25.84
a = 5.98. Call it 6.

So, by law of sines

a/sin A = b/sin B
sinB = bsinA/a = 4*.719/6 = .479
B = 28.6 deg