whats wrong in this equation

It lacks a right. to close the left{. See the code below:

begin{equation}label{eq:42}
 E_t(k,d)=left{ begin{array}{cc} k * E_{ele} + k * E_{fs} * d^2 mbox{~ if} d< d_0 ,   k * E_{ele} + k * E_{mp} * d^4 mbox{~ if} dgeq d_0
 end{array}right. %<-- this one was missing
end{equation}

Another alternative is use cases from amsmath package:

begin{equation}
 E_t(k,d)=begin{cases}
 k * E_{ele} + k * E_{fs} * d^2  & mbox{~ if} d< d_0 , 
 k * E_{ele} + k * E_{mp} * d^4 & mbox{~ if} dgeq d_0
 end{cases}
end{equation}

I add a MWE with both options:

documentclass{article}
usepackage{amsmath}
begin{document}
begin{equation}label{eq:42}
 E_t(k,d)=left{ begin{array}{cc} k * E_{ele} + k * E_{fs} * d^2 mbox{~ if} d< d_0 ,   k * E_{ele} + k * E_{mp} * d^4 mbox{~ if} dgeq d_0
 end{array}right. %<-- this one was missing
end{equation}

medskip

begin{equation}
 E_t(k,d)=begin{cases}
 k * E_{ele} + k * E_{fs} * d^2  & mbox{~ if} d< d_0 , 
 k * E_{ele} + k * E_{mp} * d^4 & mbox{~ if} dgeq d_0
 end{cases}
end{equation}

end{document}

And the output:

There are many things wrong, I'm afraid.

The main error is about TeX syntax: a left command must have a corresponding right one, in this case right., since you don't want a right fence.

On the other hand, the output is not really pretty

Let's try to correct it.

1. You should load amsmath and use its cases environment.
2. Multiplication is never denoted with an asterisk in math.
3. Textual subscripts should be upright.

documentclass{article}
usepackage{amsmath}

begin{document}

begin{equation}label{eq:42}
 E_t(k,d)=
begin{cases}
k E_{mathrm{ele}} + k E_{mathrm{fs}} d^2 & text{if } d< d_0 , 
k E_{mathrm{ele}} + k E_{mathrm{mp}} d^4 & text{if } dgeq d_0
end{cases}
end{equation}

end{document}