Use another alignment point; I show two ways, one with align
, the other one with alignat
.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
&& \phi\biggl(\,\sum_{j=1}^{r}c^{j}(e)t_{j}(p) \biggr)
&= \phi\biggl(\,\sum_{j=1}^{r} (b^{j}\circ\pi)(e)t_{j}(p)\biggr),
\\
&\text{or}& \sum_{j=1}^{r}c^{j}(e)\phi(t_{j}(e))
&= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)\phi(t_{j}(p)),
\\
&\text{or}& \sum_{j=1}^{r}c^{j}(e)(p,e_{j})
&= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)(p,e_{j}) ,
\\
&\text{or}& \biggl(p, \sum_{j=1}^{r}c^{j}(e)e_{j} \biggr)
&= \biggl(p, \sum_{j=1}^{r} (b^{j}\circ\pi)(e)e_{j} \biggr).
\end{align*}
\begin{alignat*}{2}
&&\qquad \phi\biggl(\,\sum_{j=1}^{r}c^{j}(e)t_{j}(p) \biggr)
&= \phi\biggl(\,\sum_{j=1}^{r} (b^{j}\circ\pi)(e)t_{j}(p)\biggr),
\\
&\text{or}& \sum_{j=1}^{r}c^{j}(e)\phi(t_{j}(e))
&= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)\phi(t_{j}(p)),
\\
&\text{or}& \sum_{j=1}^{r}c^{j}(e)(p,e_{j})
&= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)(p,e_{j}) ,
\\
&\text{or}& \biggl(p, \sum_{j=1}^{r}c^{j}(e)e_{j} \biggr)
&= \biggl(p, \sum_{j=1}^{r} (b^{j}\circ\pi)(e)e_{j} \biggr).
\end{alignat*}
\end{document}
Note that the outer \left(
and \right)
should better be \biggl(
and \biggr). Add
\,after
\biggl(in order not to hit the subscript. The inner
\leftand
\right` are wrong.

An alternative without alignment at the equals signs.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
& \phi\biggl(\,\sum_{j=1}^{r}c^{j}(e)t_{j}(p) \biggr)
= \phi\biggl(\,\sum_{j=1}^{r} (b^{j}\circ\pi)(e)t_{j}(p)\biggr),
\\
\text{or}\quad
& \sum_{j=1}^{r}c^{j}(e)\phi(t_{j}(e))
= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)\phi(t_{j}(p)),
\\
\text{or}\quad
& \sum_{j=1}^{r}c^{j}(e)(p,e_{j})
= \sum_{j=1}^{r} (b^{j}\circ\pi)(e)(p,e_{j}) ,
\\
\text{or}\quad
& \biggl(p, \sum_{j=1}^{r}c^{j}(e)e_{j} \biggr)
= \biggl(p, \sum_{j=1}^{r} (b^{j}\circ\pi)(e)e_{j} \biggr).
\end{align*}
\end{document}

\documentclass{...}
, the required\usepackage
's,\begin{document}
, and\end{document}
. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – samcarter_is_at_topanswers.xyz Dec 6 '16 at 21:51